### All Algebra II Resources

## Example Questions

### Example Question #1 : Using E

On the day of a child's birth, a sum of money is to be invested into a certificate of deposit (CD) that draws 6.2% annual interest compounded *continuously*. The plan is for the value of the CD to be *at least* $20,000 on the child's 18th birthday.

If the amount of money invested is to be a multiple of $1,000, 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.

### Example Question #2 : Using E

Twelve years ago, your grandma put money into a savings account for you that earns interest annually and is continuously compounded. How much money is currently in your account if she initially deposited and you have not taken any money out?

**Possible Answers:**

$24,596

$21,170

$81,030

$8,103

$10,778

**Correct answer:**

$24,596

1. Use where is the current amount, is the interest rate, is the amount of time in years since the initial deposit, and is the amount initially deposited.

2. Solve for

You currently have $24,596 in your account.

### Example Question #3 : Using E

Solve for

**Possible Answers:**

**Correct answer:**

Step 1: Achieve same bases

Step 2: Drop bases, set exponents equal to eachother

Step 3: Solve for x

### Example Question #4 : Using E

Solve for

**Possible Answers:**

**Correct answer:**

Step 1: Achieve same bases

Step 2: Drop bases, set exponents equal to eachother

Step 3: Solve for

### Example Question #5 : Using E

Solve for

**Possible Answers:**

**Correct answer:**

Step 1: Achieve same bases

Step 2: Drop bases and set exponents equal to eachother

Step 3: Solve for

### Example Question #6 : Using E

Solve for

**Possible Answers:**

**Correct answer:**

Step 1: Achieve same bases

Step 2: Drop bases and set exponents equal to eachother

Step 3: Solve for

### Example Question #7 : Using E

Solve for

**Possible Answers:**

**Correct answer:**

Step 1: Achieve same bases

Step 2: Drop bases, set exponenets equal to eachother

Step 3: Solve for

### Example Question #1 : Exponential Functions

Solve:

**Possible Answers:**

The answer does not exist.

**Correct answer:**

To solve , it is necessary to know the property of .

Since and the terms cancel due to inverse operations, the answer is what's left of the term.

The answer is:

### Example Question #8 : Using E

Simplify:

**Possible Answers:**

**Correct answer:**

In order to eliminate the natural log on both side, we will need to raise both sides as a power with a base of . This will cancel out the natural logs.

The equation will become:

Subtract on both sides.

Simplify both sides.

Divide both sides by negative five.

The answer is:

### Example Question #9 : Using E

Simplify:

**Possible Answers:**

**Correct answer:**

In order to cancel the natural logs, we will need to use as a base and raise both raise both sides as the quantity of the power.

The equation becomes:

Subtract and add three on both sides.

The equation becomes:

Use the quadratic equation to solve for the possible roots.

Simplify the quadratic equation.

The answers are: