### All Algebra II Resources

## Example Questions

### Example Question #196 : Understanding Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

In order to solve for the x-variable, we will need to raise both sides as powers of base , since the natural log has a default base of .

The equation becomes:

Add three on both sides.

Divide by four on both sides.

The equation is:

The answer is:

### Example Question #191 : Exponents

On the day of a child's birth, a sum of money is to be invested into a certificate of deposit (CD) that draws annual interest compounded *continuously*. The plan is for the value of the CD to be *at least* on the child's birthday.

If the amount of money invested is to be a multiple of , what is the *minimum* that should be invested initially, assuming that there are no further deposits or withdrawals?

**Possible Answers:**

**Correct answer:**

If we let be the initial amount invested and be the annual interest rate of the CD expressed as a decimal, then at the end of years, the amount of money that the CD will be worth can be determined by the formula

Substitute , , , and solve for .

The minimum principal to be invested initially is $6,551. However, since we are looking for the multiple of $1,000 that guarantees a minimum final balance of $20,000, we round *up* to the nearest such multiple, which is $7,000 - the correct response.