AP Precalculus Flashcards: Exponential Function Context And Data Modeling

Study Exponential Function Context And Data Modeling in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Exponential Function Context And Data Modeling

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QUESTION

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Calculate $f(3)$ for $f(x) = 4 \times (0.5)^x$ .

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ANSWER

0.5. $f(3) = 4 \times (0.5)^3 = 4 \times 0.125 = 0.5$ .

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What this deck covers

This deck focuses on Exponential Function Context And Data Modeling, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: Calculate $f(3)$ for $f(x) = 4 \times (0.5)^x$ .

Answer: 0.5. $f(3) = 4 \times (0.5)^3 = 4 \times 0.125 = 0.5$ .

Flashcard 2: State the formula for continuous exponential growth.

Answer: $A = P e^{rt}$ . Uses natural base $e$ for continuous compounding.

Flashcard 3: What is the doubling time formula in exponential growth?

Answer: $T_d = \frac{\text{ln}(2)}{\text{ln}(b)}$ . Time required for quantity to double in size.

Flashcard 4: Define an exponential decay function.

Answer: $f(x) = a \times b^x$ , $0 < b < 1$ . Decay occurs when base is between 0 and 1.

Flashcard 5: Calculate decay rate if $b = 0.9$ in $f(x) = a \times b^x$ .

Answer: 10%. Decay rate is $(1 - 0.9) = 0.1 = 10\%$ .

Flashcard 6: Determine the effect of $f(x) = a \times (b^x) + c$ when $c > 0$ .

Answer: Vertical shift up by $c$ . Positive $c$ shifts the entire graph upward.

Flashcard 7: Determine the growth factor for $f(x) = 3 \times 1.05^x$ .

Answer: 1.05. Growth factor is the base when $b > 1$ .

Flashcard 8: For $f(x) = 6 \times 0.5^x$ , what is the decay factor?

Answer: 0.5. The base represents the decay factor.

Flashcard 9: Which parameter affects horizontal shifts in $f(x) = a \times b^{x+c}$ ?

Answer: $c$ . Parameter $c$ controls horizontal translation.

Flashcard 10: What is the inverse of an exponential function?

Answer: Logarithmic function. Exponential and logarithmic functions are inverses.

Flashcard 11: Is $f(x) = 1 \times (0.5)^x$ growth or decay?

Answer: Decay. Base 0.5 is less than 1, indicating decay.

Flashcard 12: Which parameter affects horizontal shifts in $f(x) = a \times b^{x+c}$ ?

Answer: $c$ . Parameter $c$ controls horizontal translation.

Flashcard 13: For $f(x) = 9 \times 1.2^x$ , what is the growth rate?

Answer: 20%. Growth rate is $(b - 1) \times 100\%$ .

Flashcard 14: For $f(x) = 6 \times 0.5^x$ , what is the decay factor?

Answer: 0.5. The base represents the decay factor.

Flashcard 15: For $f(x) = 9 \times 1.2^x$ , what is the growth rate?

Answer: 20%. Growth rate is $(b - 1) \times 100\%$ .

Flashcard 16: What is the effect of a negative exponent in $f(x) = a \times b^{-x}$ ?

Answer: Reflect across y-axis. Negative exponent reverses the function horizontally.

Flashcard 17: Calculate the future value $A$ for $P = 1000, r = 0.08, t = 2$ .

Answer: $A = 1000 e^{0.16}$ . $A = 1000e^{0.08 \times 2} = 1000e^{0.16}$ .

Flashcard 18: State the half-life formula for exponential decay.

Answer: $N(t) = N_0 \times (\frac{1}{2})^{\frac{t}{h}}$ . Models quantity halving every $h$ time units.

Flashcard 19: What transformation occurs when $f(x) = a \times b^{x+c}$ ?

Answer: Horizontal shift left by $c$ . Adding $c$ to exponent shifts graph leftward.

Flashcard 20: Determine the growth factor for $f(x) = 3 \times 1.05^x$ .

Answer: 1.05. Growth factor is the base when $b > 1$ .

Flashcard 21: Determine the y-intercept of $f(x) = 2 \times 3^x$ .

Answer:

Y-intercept occurs when $x = 0$ .

Flashcard 22: Identify the range of $f(x) = 8 \times (1.5)^x$ .

Answer: $(0, \text{inf})$ . All exponential functions have range $(0, \infty)$ .

Flashcard 23: Calculate $f(3)$ for $f(x) = 4 \times (0.5)^x$ .

Answer: 0.5. $f(3) = 4 \times (0.5)^3 = 4 \times 0.125 = 0.5$ .

Flashcard 24: State the domain of any exponential function $f(x) = a \times b^x$ .

Answer: All real numbers. Exponential functions accept all real number inputs.

Flashcard 25: Define an exponential decay function.

Answer: $f(x) = a \times b^x$ , $0 < b < 1$ . Decay occurs when base is between 0 and 1.

Flashcard 26: Identify the range of $f(x) = 8 \times (1.5)^x$ .

Answer: $(0, \text{inf})$ . All exponential functions have range $(0, \infty)$ .

Flashcard 27: What does the variable $a$ represent in $f(x) = a \times b^x$ ?

Answer: Initial value. The coefficient $a$ is the starting amount.

Flashcard 28: What is the horizontal asymptote of $f(x) = 4 \times (0.75)^x$ ?

Answer: $y = 0$ . Exponential functions approach but never reach zero.

Flashcard 29: Identify the base in the exponential function $f(x) = 5 \times 2^x$ .

Answer:

The base is the number being raised to the power.

Flashcard 30: Is $f(x) = 1 \times (0.5)^x$ growth or decay?

Answer: Decay. Base 0.5 is less than 1, indicating decay.

Flashcard 31: State the domain of any exponential function $f(x) = a \times b^x$ .

Answer: All real numbers. Exponential functions accept all real number inputs.

Flashcard 32: Identify the effect of $f(x) = -a \times b^x$ on the graph.

Answer: Reflection over x-axis. Negative coefficient flips graph over x-axis.

Flashcard 33: State the natural base $e$ approximately.

Answer: 2.718. Euler's number, base of natural logarithm.

Flashcard 34: What is the horizontal asymptote of $f(x) = 4 \times (0.75)^x$ ?

Answer: $y = 0$ . Exponential functions approach but never reach zero.

Flashcard 35: What property does the base $b$ have in an exponential function $f(x) = a \times b^x$ ?

Answer: $b > 0$ and $b \neq 1$ . Base must be positive and not equal to 1.

Flashcard 36: Find the value of $f(2)$ for $f(x) = 2 \times 5^x$ .

Answer:

$f(2) = 2 \times 5^2 = 2 \times 25 = 50$ .

Flashcard 37: What property does the base $b$ have in an exponential function $f(x) = a \times b^x$ ?

Answer: $b > 0$ and $b \neq 1$ . Base must be positive and not equal to 1.

Flashcard 38: What does the parameter $r$ represent in $A = P e^{rt}$ ?

Answer: Rate of growth or decay. The exponent controls growth or decay rate.

Flashcard 39: For $f(x) = 5 \times (0.8)^x$ , what is the percentage decay rate?

Answer: 20%. Decay rate is $(1 - b) \times 100\%$ .

Flashcard 40: What is the effect of $a$ in $f(x) = a \times b^x$ on the graph?

Answer: Vertical stretch/compression. Parameter $a$ scales the function vertically.

Flashcard 41: What is the formula for finding the rate $r$ in $A = P e^{rt}$ ?

Answer: $r = \frac{1}{t} \text{ln}(\frac{A}{P})$ . Solved from $A = Pe^{rt}$ for rate $r$ .

Flashcard 42: What transformation occurs when $f(x) = a \times b^{x+c}$ ?

Answer: Horizontal shift left by $c$ . Adding $c$ to exponent shifts graph leftward.

Flashcard 43: What is the effect of a negative exponent in $f(x) = a \times b^{-x}$ ?

Answer: Reflect across y-axis. Negative exponent reverses the function horizontally.

Flashcard 44: What is the range for an exponential decay function?

Answer: $(0, a)$ if $a > 0$ . Decay functions approach zero from above.

Flashcard 45: Calculate decay rate if $b = 0.9$ in $f(x) = a \times b^x$ .

Answer: 10%. Decay rate is $(1 - 0.9) = 0.1 = 10\%$ .

Flashcard 46: What transformation is applied in $f(x) = a \times b^{x} + d$ ?

Answer: Vertical shift by $d$ . Adding $d$ moves the graph up or down.

Flashcard 47: Determine the y-intercept of $f(x) = 2 \times 3^x$ .

Answer:

Y-intercept occurs when $x = 0$ .

Flashcard 48: What transformation is applied in $f(x) = a \times b^{x} + d$ ?

Answer: Vertical shift by $d$ . Adding $d$ moves the graph up or down.

Flashcard 49: State the half-life formula for exponential decay.

Answer: $N(t) = N_0 \times (\frac{1}{2})^{\frac{t}{h}}$ . Models quantity halving every $h$ time units.

Flashcard 50: Find the value of $f(2)$ for $f(x) = 2 \times 5^x$ .

Answer:

$f(2) = 2 \times 5^2 = 2 \times 25 = 50$ .

Flashcard 51: What is the doubling time formula in exponential growth?

Answer: $T_d = \frac{\text{ln}(2)}{\text{ln}(b)}$ . Time required for quantity to double in size.

Flashcard 52: Determine the effect of $f(x) = a \times (b^x) + c$ when $c > 0$ .

Answer: Vertical shift up by $c$ . Positive $c$ shifts the entire graph upward.

Flashcard 53: Identify the effect of $f(x) = -a \times b^x$ on the graph.

Answer: Reflection over x-axis. Negative coefficient flips graph over x-axis.

Flashcard 54: For $f(x) = 5 \times (0.8)^x$ , what is the percentage decay rate?

Answer: 20%. Decay rate is $(1 - b) \times 100\%$ .

Flashcard 55: What is the inverse of an exponential function?

Answer: Logarithmic function. Exponential and logarithmic functions are inverses.

Flashcard 56: What is the general form of an exponential function?

Answer: $f(x) = a \times b^x$ . Standard form with initial value $a$ and base $b$ .

Flashcard 57: What is the value of $f(0)$ for $f(x) = a \times b^x$ ?

Answer: $a$ . When $x = 0$ , $b^0 = 1$ , so $f(0) = a$ .

Flashcard 58: Identify the base in the exponential function $f(x) = 5 \times 2^x$ .

Answer:

The base is the number being raised to the power.

Flashcard 59: Find the initial value of the function $f(x) = 3 \times 4^x$ .

Answer:

Initial value is coefficient $a$ when $x = 0$ .

Flashcard 60: What does the variable $a$ represent in $f(x) = a \times b^x$ ?

Answer: Initial value. The coefficient $a$ is the starting amount.

Flashcard 61: Find the initial value of the function $f(x) = 3 \times 4^x$ .

Answer:

Initial value is coefficient $a$ when $x = 0$ .

Flashcard 62: What does the parameter $r$ represent in $A = P e^{rt}$ ?

Answer: Rate of growth or decay. The exponent controls growth or decay rate.

Flashcard 63: What is the exponential growth factor if $b = 1.1$ ?

Answer: 1.1. Growth factor is the base $b$ when $b > 1$ .

Flashcard 64: Calculate the future value $A$ for $P = 1000, r = 0.08, t = 2$ .

Answer: $A = 1000 e^{0.16}$ . $A = 1000e^{0.08 \times 2} = 1000e^{0.16}$ .

Flashcard 65: What is the range for an exponential decay function?

Answer: $(0, a)$ if $a > 0$ . Decay functions approach zero from above.

Flashcard 66: What is the formula for finding the rate $r$ in $A = P e^{rt}$ ?

Answer: $r = \frac{1}{t} \text{ln}(\frac{A}{P})$ . Solved from $A = Pe^{rt}$ for rate $r$ .

Flashcard 67: What is the effect of $a$ in $f(x) = a \times b^x$ on the graph?

Answer: Vertical stretch/compression. Parameter $a$ scales the function vertically.

Flashcard 68: What is the value of $f(0)$ for $f(x) = a \times b^x$ ?

Answer: $a$ . When $x = 0$ , $b^0 = 1$ , so $f(0) = a$ .

Flashcard 69: State the formula for continuous exponential growth.

Answer: $A = P e^{rt}$ . Uses natural base $e$ for continuous compounding.

Flashcard 70: State the natural base $e$ approximately.

Answer: 2.718. Euler's number, base of natural logarithm.

Flashcard 71: What is the exponential growth factor if $b = 1.1$ ?

Answer: 1.1. Growth factor is the base $b$ when $b > 1$ .

AP Precalculus Flashcards: Exponential Function Context And Data Modeling

Exponential Function Context And Data Modeling

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: Calculate f(3)f(3)f(3) for f(x)=4×(0.5)xf(x) = 4 \times (0.5)^xf(x)=4×(0.5)x.

Flashcard 2: State the formula for continuous exponential growth.

Flashcard 3: What is the doubling time formula in exponential growth?

Flashcard 4: Define an exponential decay function.

Flashcard 5: Calculate decay rate if b=0.9b = 0.9b=0.9 in f(x)=a×bxf(x) = a \times b^xf(x)=a×bx.

Flashcard 6: Determine the effect of f(x)=a×(bx)+cf(x) = a \times (b^x) + cf(x)=a×(bx)+c when c>0c > 0c>0.

Flashcard 7: Determine the growth factor for f(x)=3×1.05xf(x) = 3 \times 1.05^xf(x)=3×1.05x.

Flashcard 8: For f(x)=6×0.5xf(x) = 6 \times 0.5^xf(x)=6×0.5x, what is the decay factor?

Flashcard 9: Which parameter affects horizontal shifts in f(x)=a×bx+cf(x) = a \times b^{x+c}f(x)=a×bx+c?

Flashcard 10: What is the inverse of an exponential function?

Flashcard 11: Is f(x)=1×(0.5)xf(x) = 1 \times (0.5)^xf(x)=1×(0.5)x growth or decay?

Flashcard 12: Which parameter affects horizontal shifts in f(x)=a×bx+cf(x) = a \times b^{x+c}f(x)=a×bx+c?

Flashcard 13: For f(x)=9×1.2xf(x) = 9 \times 1.2^xf(x)=9×1.2x, what is the growth rate?

Flashcard 14: For f(x)=6×0.5xf(x) = 6 \times 0.5^xf(x)=6×0.5x, what is the decay factor?

Flashcard 15: For f(x)=9×1.2xf(x) = 9 \times 1.2^xf(x)=9×1.2x, what is the growth rate?

Flashcard 16: What is the effect of a negative exponent in f(x)=a×b−xf(x) = a \times b^{-x}f(x)=a×b−x?

Flashcard 17: Calculate the future value AAA for P=1000,r=0.08,t=2P = 1000, r = 0.08, t = 2P=1000,r=0.08,t=2.

Flashcard 18: State the half-life formula for exponential decay.

Flashcard 19: What transformation occurs when f(x)=a×bx+cf(x) = a \times b^{x+c}f(x)=a×bx+c?

Flashcard 20: Determine the growth factor for f(x)=3×1.05xf(x) = 3 \times 1.05^xf(x)=3×1.05x.

Flashcard 21: Determine the y-intercept of f(x)=2×3xf(x) = 2 \times 3^xf(x)=2×3x.

Flashcard 22: Identify the range of f(x)=8×(1.5)xf(x) = 8 \times (1.5)^xf(x)=8×(1.5)x.

Flashcard 23: Calculate f(3)f(3)f(3) for f(x)=4×(0.5)xf(x) = 4 \times (0.5)^xf(x)=4×(0.5)x.

Flashcard 24: State the domain of any exponential function f(x)=a×bxf(x) = a \times b^xf(x)=a×bx.

Flashcard 25: Define an exponential decay function.

Flashcard 26: Identify the range of f(x)=8×(1.5)xf(x) = 8 \times (1.5)^xf(x)=8×(1.5)x.

Flashcard 27: What does the variable aaa represent in f(x)=a×bxf(x) = a \times b^xf(x)=a×bx?

Flashcard 28: What is the horizontal asymptote of f(x)=4×(0.75)xf(x) = 4 \times (0.75)^xf(x)=4×(0.75)x?

Flashcard 29: Identify the base in the exponential function f(x)=5×2xf(x) = 5 \times 2^xf(x)=5×2x.

Flashcard 30: Is f(x)=1×(0.5)xf(x) = 1 \times (0.5)^xf(x)=1×(0.5)x growth or decay?

Flashcard 31: State the domain of any exponential function f(x)=a×bxf(x) = a \times b^xf(x)=a×bx.

Flashcard 32: Identify the effect of f(x)=−a×bxf(x) = -a \times b^xf(x)=−a×bx on the graph.

Flashcard 33: State the natural base eee approximately.

Flashcard 34: What is the horizontal asymptote of f(x)=4×(0.75)xf(x) = 4 \times (0.75)^xf(x)=4×(0.75)x?

Flashcard 35: What property does the base bbb have in an exponential function f(x)=a×bxf(x) = a \times b^xf(x)=a×bx?

Flashcard 36: Find the value of f(2)f(2)f(2) for f(x)=2×5xf(x) = 2 \times 5^xf(x)=2×5x.

Flashcard 37: What property does the base bbb have in an exponential function f(x)=a×bxf(x) = a \times b^xf(x)=a×bx?

Flashcard 38: What does the parameter rrr represent in A=PertA = P e^{rt}A=Pert?

Flashcard 39: For f(x)=5×(0.8)xf(x) = 5 \times (0.8)^xf(x)=5×(0.8)x, what is the percentage decay rate?

Flashcard 40: What is the effect of aaa in f(x)=a×bxf(x) = a \times b^xf(x)=a×bx on the graph?

Flashcard 41: What is the formula for finding the rate rrr in A=PertA = P e^{rt}A=Pert?

Flashcard 42: What transformation occurs when f(x)=a×bx+cf(x) = a \times b^{x+c}f(x)=a×bx+c?

Flashcard 43: What is the effect of a negative exponent in f(x)=a×b−xf(x) = a \times b^{-x}f(x)=a×b−x?

Flashcard 44: What is the range for an exponential decay function?

Flashcard 45: Calculate decay rate if b=0.9b = 0.9b=0.9 in f(x)=a×bxf(x) = a \times b^xf(x)=a×bx.

Flashcard 46: What transformation is applied in f(x)=a×bx+df(x) = a \times b^{x} + df(x)=a×bx+d?

Flashcard 47: Determine the y-intercept of f(x)=2×3xf(x) = 2 \times 3^xf(x)=2×3x.

Flashcard 48: What transformation is applied in f(x)=a×bx+df(x) = a \times b^{x} + df(x)=a×bx+d?

Flashcard 49: State the half-life formula for exponential decay.

Flashcard 50: Find the value of f(2)f(2)f(2) for f(x)=2×5xf(x) = 2 \times 5^xf(x)=2×5x.

Flashcard 51: What is the doubling time formula in exponential growth?

Flashcard 52: Determine the effect of f(x)=a×(bx)+cf(x) = a \times (b^x) + cf(x)=a×(bx)+c when c>0c > 0c>0.

Flashcard 53: Identify the effect of f(x)=−a×bxf(x) = -a \times b^xf(x)=−a×bx on the graph.

Flashcard 54: For f(x)=5×(0.8)xf(x) = 5 \times (0.8)^xf(x)=5×(0.8)x, what is the percentage decay rate?

Flashcard 55: What is the inverse of an exponential function?

Flashcard 56: What is the general form of an exponential function?

Flashcard 57: What is the value of f(0)f(0)f(0) for f(x)=a×bxf(x) = a \times b^xf(x)=a×bx?

Flashcard 58: Identify the base in the exponential function f(x)=5×2xf(x) = 5 \times 2^xf(x)=5×2x.

Flashcard 59: Find the initial value of the function f(x)=3×4xf(x) = 3 \times 4^xf(x)=3×4x.

Flashcard 60: What does the variable aaa represent in f(x)=a×bxf(x) = a \times b^xf(x)=a×bx?

Flashcard 61: Find the initial value of the function f(x)=3×4xf(x) = 3 \times 4^xf(x)=3×4x.

Flashcard 62: What does the parameter rrr represent in A=PertA = P e^{rt}A=Pert?

Flashcard 63: What is the exponential growth factor if b=1.1b = 1.1b=1.1?

Flashcard 64: Calculate the future value AAA for P=1000,r=0.08,t=2P = 1000, r = 0.08, t = 2P=1000,r=0.08,t=2.

Flashcard 65: What is the range for an exponential decay function?

Flashcard 66: What is the formula for finding the rate rrr in A=PertA = P e^{rt}A=Pert?

Flashcard 67: What is the effect of aaa in f(x)=a×bxf(x) = a \times b^xf(x)=a×bx on the graph?

Flashcard 68: What is the value of f(0)f(0)f(0) for f(x)=a×bxf(x) = a \times b^xf(x)=a×bx?

Flashcard 69: State the formula for continuous exponential growth.

Flashcard 70: State the natural base eee approximately.

Flashcard 71: What is the exponential growth factor if b=1.1b = 1.1b=1.1?

Flashcard 1: Calculate $f(3)$ for $f(x) = 4 \times (0.5)^x$ .

Flashcard 5: Calculate decay rate if $b = 0.9$ in $f(x) = a \times b^x$ .

Flashcard 6: Determine the effect of $f(x) = a \times (b^x) + c$ when $c > 0$ .

Flashcard 7: Determine the growth factor for $f(x) = 3 \times 1.05^x$ .

Flashcard 8: For $f(x) = 6 \times 0.5^x$ , what is the decay factor?

Flashcard 9: Which parameter affects horizontal shifts in $f(x) = a \times b^{x+c}$ ?

Flashcard 11: Is $f(x) = 1 \times (0.5)^x$ growth or decay?

Flashcard 12: Which parameter affects horizontal shifts in $f(x) = a \times b^{x+c}$ ?

Flashcard 13: For $f(x) = 9 \times 1.2^x$ , what is the growth rate?

Flashcard 14: For $f(x) = 6 \times 0.5^x$ , what is the decay factor?

Flashcard 15: For $f(x) = 9 \times 1.2^x$ , what is the growth rate?

Flashcard 16: What is the effect of a negative exponent in $f(x) = a \times b^{-x}$ ?

Flashcard 17: Calculate the future value $A$ for $P = 1000, r = 0.08, t = 2$ .

Flashcard 19: What transformation occurs when $f(x) = a \times b^{x+c}$ ?

Flashcard 20: Determine the growth factor for $f(x) = 3 \times 1.05^x$ .

Flashcard 21: Determine the y-intercept of $f(x) = 2 \times 3^x$ .

Flashcard 22: Identify the range of $f(x) = 8 \times (1.5)^x$ .

Flashcard 23: Calculate $f(3)$ for $f(x) = 4 \times (0.5)^x$ .

Flashcard 24: State the domain of any exponential function $f(x) = a \times b^x$ .

Flashcard 26: Identify the range of $f(x) = 8 \times (1.5)^x$ .

Flashcard 27: What does the variable $a$ represent in $f(x) = a \times b^x$ ?

Flashcard 28: What is the horizontal asymptote of $f(x) = 4 \times (0.75)^x$ ?

Flashcard 29: Identify the base in the exponential function $f(x) = 5 \times 2^x$ .

Flashcard 30: Is $f(x) = 1 \times (0.5)^x$ growth or decay?

Flashcard 31: State the domain of any exponential function $f(x) = a \times b^x$ .

Flashcard 32: Identify the effect of $f(x) = -a \times b^x$ on the graph.

Flashcard 33: State the natural base $e$ approximately.

Flashcard 34: What is the horizontal asymptote of $f(x) = 4 \times (0.75)^x$ ?

Flashcard 35: What property does the base $b$ have in an exponential function $f(x) = a \times b^x$ ?

Flashcard 36: Find the value of $f(2)$ for $f(x) = 2 \times 5^x$ .

Flashcard 37: What property does the base $b$ have in an exponential function $f(x) = a \times b^x$ ?

Flashcard 38: What does the parameter $r$ represent in $A = P e^{rt}$ ?

Flashcard 39: For $f(x) = 5 \times (0.8)^x$ , what is the percentage decay rate?

Flashcard 40: What is the effect of $a$ in $f(x) = a \times b^x$ on the graph?

Flashcard 41: What is the formula for finding the rate $r$ in $A = P e^{rt}$ ?

Flashcard 42: What transformation occurs when $f(x) = a \times b^{x+c}$ ?

Flashcard 43: What is the effect of a negative exponent in $f(x) = a \times b^{-x}$ ?

Flashcard 45: Calculate decay rate if $b = 0.9$ in $f(x) = a \times b^x$ .

Flashcard 46: What transformation is applied in $f(x) = a \times b^{x} + d$ ?

Flashcard 47: Determine the y-intercept of $f(x) = 2 \times 3^x$ .

Flashcard 48: What transformation is applied in $f(x) = a \times b^{x} + d$ ?

Flashcard 50: Find the value of $f(2)$ for $f(x) = 2 \times 5^x$ .

Flashcard 52: Determine the effect of $f(x) = a \times (b^x) + c$ when $c > 0$ .

Flashcard 53: Identify the effect of $f(x) = -a \times b^x$ on the graph.

Flashcard 54: For $f(x) = 5 \times (0.8)^x$ , what is the percentage decay rate?

Flashcard 57: What is the value of $f(0)$ for $f(x) = a \times b^x$ ?

Flashcard 58: Identify the base in the exponential function $f(x) = 5 \times 2^x$ .

Flashcard 59: Find the initial value of the function $f(x) = 3 \times 4^x$ .

Flashcard 60: What does the variable $a$ represent in $f(x) = a \times b^x$ ?

Flashcard 61: Find the initial value of the function $f(x) = 3 \times 4^x$ .

Flashcard 62: What does the parameter $r$ represent in $A = P e^{rt}$ ?

Flashcard 63: What is the exponential growth factor if $b = 1.1$ ?

Flashcard 64: Calculate the future value $A$ for $P = 1000, r = 0.08, t = 2$ .

Flashcard 66: What is the formula for finding the rate $r$ in $A = P e^{rt}$ ?

Flashcard 67: What is the effect of $a$ in $f(x) = a \times b^x$ on the graph?

Flashcard 68: What is the value of $f(0)$ for $f(x) = a \times b^x$ ?

Flashcard 70: State the natural base $e$ approximately.

Flashcard 71: What is the exponential growth factor if $b = 1.1$ ?