This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. In an exponential function y = $a·b^x$, the base b tells you whether it's growth or decay: if b > 1 (bigger than 1), the function is growing exponentially; if 0 < b < 1 (between 0 and 1), it's decaying. The initial value a is what you start with when x = 0. For the function P(t) = $800(1.03)^t$, the base is 1.03. To find the percent rate, we calculate r = 1.03 - 1 = 0.03. Converting to percent: 0.03 × 100% = 3%. Since 1.03 is greater than 1, this is growth, specifically 3% growth per year. Choice B correctly identifies the percent rate as 3% growth by recognizing that the base 1.03 represents a 3% annual increase. Excellent! Choice C makes a common percent mistake: the base 1.03 doesn't mean 103% growth—it means 3% growth! The 1 represents 'what you already have' (100%), and the 0.03 is the additional 3%, for a total of 103% of the previous amount (which is 3% growth). To find the percent rate: (1) Identify the base b, (2) Subtract 1: r = b - 1, (3) Convert to percent: multiply by 100. Example: base is 1.03, so r = 1.03 - 1 = 0.03 = 3%. For decay like 0.97: r = 0.97 - 1 = -0.03 = -3%, which we call '3% decay.' Easy!

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. Real-world clue: 'percent interest' or 'percent increase' means exponential growth with that as your r. 'Percent depreciation' or 'percent decrease' means exponential decay. The problem language often tells you what type and what rate directly—you just translate to mathematical form! The context tells us initial value is 1000 and rate is 10% increase. Converting the rate to decimal: 10% = 0.10. The growth factor is b = 1 + 0.10 = 1.10. So the exponential function is y = $1000·(1.10)^t$. We can also write this as y = 1000(1 + $0.10)^t$ to show the rate explicitly! Choice B correctly identifies the function as $y=1000(1.10)^t$ by showing correct reasoning. Excellent! Choice A confuses growth with decay (or vice versa): since the base 0.10 is less than 1, this is decay, not growth. An easy way to remember: bases bigger than 1 mean growing, bases between 0 and 1 mean shrinking! The form y = a(1 + $r)^x$ makes the rate super obvious: if you see y = 500(1 + $0.08)^t$, you can read the rate right off—it's 0.08 = 8%. But if you see y = $500(1.08)^t$, you have to subtract 1 from the base: 1.08 - 1 = 0.08 = 8%. Same rate, just written differently!

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. The key difference between growth factor and growth rate: the factor b is what you multiply by each time (like 1.03), while the rate r is how much it's changing by percent (like 3%). They're related by b = 1 + r, so knowing one gives you the other! Looking at the function V(t) = $25000(0.88)^t$, we check the base: 0.88 is less than 1, which means this is exponential decay. Think of it this way: each time t increases by 1, V is multiplied by 0.88, so V is getting smaller—that's decay! Choice C correctly identifies this as exponential decay because the base 0.88 < 1. Excellent! Choice A confuses growth with decay: since the base 0.88 is less than 1, this is decay, not growth. An easy way to remember: bases bigger than 1 mean growing, bases between 0 and 1 mean shrinking! Here's your growth/decay decision tree: (1) Look at the base b, (2) Is b > 1? That's growth. Is 0 < b < 1? That's decay. Is b = 1? No change. That's it! For example, 1.07 > 1 so growth, 0.94 < 1 so decay, 1.00 = 1 so constant.

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. In an exponential function y = $a·b^x$, the base b tells you whether it's growth or decay: if b > 1 (bigger than 1), the function is growing exponentially; if 0 < b < 1 (between 0 and 1), it's decaying. The initial value a is what you start with when x = 0. Looking at each function, we check the bases: A has base 1.08 > 1 (growth), B has base 0.90 < 1 (decay), C has base 1.00 = 1 (constant), D has base 1.15 > 1 (growth). Only choice B has a base less than 1, making it exponential decay. Choice B correctly identifies y = $100(0.90)^t$ as exponential decay because the base 0.90 < 1. Excellent! Choices A and D have bases greater than 1, so they represent growth, not decay. Choice C has base exactly 1, which means no change—it stays constant at 100. Here's your growth/decay decision tree: (1) Look at the base b, (2) Is b > 1? That's growth. Is 0 < b < 1? That's decay. Is b = 1? No change. That's it! For example, 1.07 > 1 so growth, 0.94 < 1 so decay, 1.00 = 1 so constant.

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. To find the percent growth or decay rate from the base, use the formula r = b - 1 and convert to percent: if b = 1.05, then r = 1.05 - 1 = 0.05 = 5% growth. If b = 0.95, then r = 0.95 - 1 = -0.05 = 5% decay (we usually just say '5% decay' and understand it's a decrease). For the function M(t) = $1000(0.80)^t$, the base is 0.80. To find the percent rate, we calculate r = 0.80 - 1 = -0.20. Converting to percent: -0.20 × 100% = -20%. Since 0.80 is less than 1, this is decay, specifically 20% decay per hour. Choice D correctly identifies the percent rate as 20% decay by showing correct reasoning. Excellent! Choice B gives the growth factor (b = 0.80) when the question asks for the growth rate (r = 20% decay). Remember: factor is what you multiply by, rate is the percent change. They're related by b = 1 + r! The form y = a(1 + $r)^x$ makes the rate super obvious: if you see y = 500(1 + $0.08)^t$, you can read the rate right off—it's 0.08 = 8%. But if you see y = $500(1.08)^t$, you have to subtract 1 from the base: 1.08 - 1 = 0.08 = 8%. Same rate, just written differently!

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. The key difference between growth factor and growth rate: the factor b is what you multiply by each time (like 1.03), while the rate r is how much it's changing by percent (like 3%). They're related by b = 1 + r, so knowing one gives you the other! For the function y = $800·(1.03)^x$, the base is 1.03. To find the percent rate, we calculate r = 1.03 - 1 = 0.03 as decimal. Converting to percent: 0.03 × 100% = 3%. Since 1.03 is greater than 1, this is growth, specifically 3% growth per unit in x. Choice B correctly identifies the percent rate as 3% by showing correct reasoning. Excellent! Choice C makes a common percent mistake: the base 1.03 doesn't mean 103% growth—it means 3% growth! The 1 represents 'what you already have' (100%), and the 0.03 is the additional 3%, for a total of 103% of the previous amount (which is 3% growth). Don't confuse the factor with the rate: if something grows by 5% per year, the growth RATE is 5% (r = 0.05), but the growth FACTOR is 1.05 (b = 1.05). Each year you have 105% of what you had (100% + 5%), which means multiplying by 1.05.

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. In an exponential function y = $a·b^x$, the base b tells you whether it's growth or decay: if b > 1 (bigger than 1), the function is growing exponentially; if 0 < b < 1 (between 0 and 1), it's decaying. The initial value a is what you start with when x = 0. Looking at the function A(t) = $1000(1.01)^{12t}$, notice that the exponent is 12t, not just t. Since t is in years and the exponent includes 12t, this means we're compounding 12 times per year (monthly). The base 1.01 applies to each monthly period, so r = 1.01 - 1 = 0.01 = 1% per month. Choice A correctly identifies the monthly interest rate as 1% per month by recognizing that the base 1.01 applies to each of the 12 compounding periods per year. Excellent! Choice B might think that since there are 12 months, the rate is 12%, but that would be the approximate annual rate, not the monthly rate. The base 1.01 tells us each month the balance is multiplied by 1.01, which is 1% monthly growth. The form y = a(1 + $r)^{nt}$ is common for compound interest, where n is the number of times per year interest is compounded. Here, with A(t) = $1000(1.01)^{12t}$, we can see n = 12 (monthly) and the monthly rate is 1% since the base is 1.01.

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. To find the percent growth or decay rate from the base, use the formula r = b - 1 and convert to percent: if b = 1.05, then r = 1.05 - 1 = 0.05 = 5% growth. If b = 0.95, then r = 0.95 - 1 = -0.05 = 5% decay (we usually just say '5% decay' and understand it's a decrease). For the function V(t) = $1200(0.90)^t$, the base is 0.90. To find the percent rate, we calculate r = 0.90 - 1 = -0.10. Converting to percent: -0.10 × 100% = -10%. Since 0.90 is less than 1, this is decay, specifically 10% decay (depreciation) per year. Choice B correctly identifies the percent rate as 10% depreciation by calculating 1 - 0.90 = 0.10 = 10% decrease per year. Excellent! Choice A gives the growth factor (b = 0.90) when the question asks for the depreciation rate. Remember: if the base is 0.90, that means you keep 90% of the value each year, which is a 10% loss, not a 90% loss! Real-world clue: 'percent interest' or 'percent increase' means exponential growth with that as your r. 'Percent depreciation' or 'percent decrease' means exponential decay. The problem language often tells you what type and what rate directly—you just translate to mathematical form!

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. To find the percent growth or decay rate from the base, use the formula r = b - 1 and convert to percent: if b = 1.05, then r = 1.05 - 1 = 0.05 = 5% growth. If b = 0.95, then r = 0.95 - 1 = -0.05 = 5% decay (we usually just say '5% decay' and understand it's a decrease). For the function y = 400(1 - $0.12)^x$, we first simplify: 1 - 0.12 = 0.88, so y = $400(0.88)^x$. The base is 0.88. To find the percent rate, we calculate r = 0.88 - 1 = -0.12. Converting to percent: -0.12 × 100% = -12%. Since 0.88 is less than 1, this is decay, specifically 12% decay per unit x. Choice A correctly identifies the percent rate as 12% decay by recognizing that (1 - 0.12) = 0.88 represents keeping 88% of the quantity, which is a 12% decrease. Excellent! Choice D gives the wrong rate: the base 0.88 means we keep 88% each time, which is a 12% loss, not an 88% loss! Remember to subtract from 1 to find the decay rate. The form y = a(1 - $r)^x$ makes the decay rate super obvious: if you see y = 500(1 - $0.12)^t$, you can read the rate right off—it's 0.12 = 12% decay. This form explicitly shows what percent is being lost each time period!

This question tests your understanding of exponential functions and how to identify whether they represent growth or decay and what the percent rate of change is. To find the percent growth or decay rate from the base, use the formula r = b - 1 and convert to percent: if b = 1.05, then r = 1.05 - 1 = 0.05 = 5% growth. If b = 0.95, then r = 0.95 - 1 = -0.05 = 5% decay (we usually just say '5% decay' and understand it's a decrease). For the function A(t) = $1000(1.05)^t$, the base is 1.05. To find the percent rate, we calculate r = 1.05 - 1 = 0.05. Converting to percent: 0.05 × 100% = 5%. Since 1.05 is greater than 1, this is growth, specifically 5% growth per year. Choice B correctly identifies the percent rate as 5% growth per year by showing that 1.05 = 1 + 0.05, which represents 5% growth. Excellent! Choice C makes a common percent mistake: the base 1.05 doesn't mean 105% growth—it means 5% growth! The 1 represents 'what you already have' (100%), and the 0.05 is the additional 5%, for a total of 105% of the previous amount (which is 5% growth). To find the percent rate: (1) Identify the base b = 1.05, (2) Subtract 1: r = 1.05 - 1 = 0.05, (3) Convert to percent: 0.05 × 100 = 5%. Example: base is 1.05, so r = 1.05 - 1 = 0.05 = 5%. Easy!