### All High School Math Resources

## Example Questions

### Example Question #6 : Solving Exponential Functions

Solve the equation for .

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

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:**

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:**

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

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:**

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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