High School Math : Solving and Graphing Exponential Equations

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #6 : Solving Exponential Functions

Solve the equation for .

Possible Answers:

Correct answer:

Explanation:

Begin by recognizing that both sides of the equation have a root term of .

Using the power rule, we can set the exponents equal to each other.

Example Question #16 : Solving Exponential Equations

The population of a certain bacteria increases exponentially according to the following equation:

where P represents the total population and t represents time in minutes.

How many minutes does it take for the bacteria's population to reach 48,000?

Possible Answers:

Correct answer:

Explanation:

The question gives us P (48,000) and asks us to find t (time). We can substitute for P and start to solve for t:

Now we have to isolate t by taking the natural log of both sides:

And since , t can easily be isolated:

Note: does not equal . You have to perform the log operation first before dividing.

Example Question #7 : Solving Exponential Functions

Solve the equation for .

Possible Answers:

 

 

 

 

Correct answer:

 

Explanation:

Begin by recognizing that both sides of the equation have the same root term, .

We can use the power rule to combine exponents.

Set the exponents equal to each other.

Example Question #17 : Solving Exponential Equations

Solve for :

Possible Answers:

Correct answer:

Explanation:

Pull an  out of the left side of the equation.

Use the difference of squares technique to factor the expression in parentheses.

Any number that causes one of the terms , or  to equal  is a solution to the equation. These are , and , respectively.

Example Question #1 : Graphing Exponential Functions

Find the -intercept(s) of .

Possible Answers:

This function does not cross the -axis.

Correct answer:

Explanation:

To find the -intercept, set  in the equation and solve.

Example Question #2 : Graphing Exponential Functions

Find the -intercept(s) of .

Possible Answers:

 and 

Correct answer:

Explanation:

To find the -intercept(s) of , set the  value equal to zero and solve.

Example Question #3 : Graphing Exponential Functions

Find the -intercept(s) of .

Possible Answers:

 and 

 and 

Correct answer:

 and 

Explanation:

To find the -intercept(s) of , we need to set the numerator equal to zero and solve.

First, notice that  can be factored into . Now set that equal to zero: .

Since we have two sets in parentheses, there are two separate  values that can cause our equation to equal zero: one where  and one where .

Solve for each value:

and 

.

Therefore there are two -interecpts:  and .

Example Question #4 : Graphing Exponential Functions

Find the -intercept(s) of .

Possible Answers:

 or 

The function does not cross the -axis.

Correct answer:

Explanation:

To find the -intercept(s) of , we need to set the numerator equal to zero.

That means .

The best way to solve for a funky equation like this is to graph it in your calculator and calculate the roots. The result is .

 

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