### All High School Math Resources

## Example Questions

### Example Question #11 : Solving Exponential Equations

What are the x-intercepts of the equation?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

There are no y-intercepts.

**Correct answer:**

To find the y-intercept, set and solve.

### Example Question #13 : Solving Exponential Equations

What are the y-intercepts of this equation?

**Possible Answers:**

There are no y-intercepts for the equation.

**Correct answer:**

To find the y-intercept, set and solve.

### Example Question #14 : Solving Exponential Equations

What are the x-intercepts of the equation?

**Possible Answers:**

There are no horizontal asymptotes.

**Correct answer:**

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?

**Possible Answers:**

There are no real x-intercepts.

There are no x-intercepts.

**Correct answer:**

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

### 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.