# High School Math : Exponents

## Example Questions

### Example Question #11 : Solving Exponential Equations

What are the x-intercepts of the equation?

Explanation:

To find the x-intercepts, set the numerator equal to zero and solve.

We can simplify from here:

Now we need to rationalize. Because we have a square root on the bottom, we need to get rid of it. Since , we can multiply  to get rid of the radical in the denominator.

Since we took a square root, remember that our answer can be either positive or negative, as a positive squared is positive and a negative squared is also positive.

### Example Question #12 : Solving Exponential Equations

What are the y-intercepts of this equation?

There are no y-intercepts.

Explanation:

To find the y-intercept, set  and solve.

### Example Question #13 : Solving Exponential Equations

What are the y-intercepts of this equation?

There are no y-intercepts for the equation.

Explanation:

To find the y-intercept, set  and solve.

### Example Question #14 : Solving Exponential Equations

What are the x-intercepts of the equation?

There are no horizontal asymptotes.

Explanation:

To find the x-intercepts, we set the numerator equal to zero and solve.

However, the square root of a number can be both positive and negative.

Therefore the roots will be

### Example Question #15 : Solving Exponential Equations

What are the x-intercepts of the equation?

There are no real x-intercepts.

There are no x-intercepts.

Explanation:

To find the x-intercepts, set the numerator equal to zero.

### Example Question #6 : Solving Exponential Functions

Solve the equation for .

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?

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 .

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 :

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 .