# Algebra II : Using e

## Example Questions

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### Example Question #1 : 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?

$21,170$8,103

$24,596$81,030

$10,778 Correct answer:$24,596

Explanation:

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 #2 : Using E

Solve for

Explanation:

Step 1: Achieve same bases

Step 2: Drop bases, set exponents equal to eachother

Step 3: Solve for x

### Example Question #3 : Using E

Solve for

Explanation:

Step 1: Achieve same bases

Step 2: Drop bases, set exponents equal to eachother

Step 3: Solve for

### Example Question #4 : Using E

Solve for

Explanation:

Step 1: Achieve same bases

Step 2: Drop bases and set exponents equal to eachother

Step 3: Solve for

### Example Question #191 : Understanding Exponents

Solve for

Explanation:

Step 1: Achieve same bases

Step 2: Drop bases and set exponents equal to eachother

Step 3: Solve for

### Example Question #192 : Understanding Exponents

Solve for

Explanation:

Step 1: Achieve same bases

Step 2: Drop bases, set exponenets equal to eachother

Step 3: Solve for

### Example Question #1 : Exponential Functions

Solve:

Explanation:

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.

### Example Question #193 : Understanding Exponents

Simplify:

Explanation:

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.

### Example Question #194 : Understanding Exponents

Simplify:

Explanation:

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.

### Example Question #195 : Understanding Exponents

Simplify:

Explanation:

In order to get rid of the natural log, we will need to use the exponential term  as a base and raise both sides as the powers using this base.

The equation becomes:

Subtract nine from both sides.

Divide by three on both sides.

Simplify both sides.