Algebra II : Using e

Study concepts, example questions & explanations for Algebra II

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Example Questions

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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:

Explanation:

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

$8,103

$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 

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

Explanation:

Step 1: Achieve same bases

  

Step 2: Drop bases and set exponents equal to eachother

Step 3: Solve for 

Example Question #5 : Using E

Solve for 

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

Step 1: Achieve same bases

Step 2: Drop bases, set exponenets equal to eachother 

Step 3: Solve for 

Example Question #7 : Using E

Solve:  

Possible Answers:

The answer does not exist.

Correct answer:

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.

The answer is:  

Example Question #8 : Using E

Simplify:  

Possible Answers:

Correct answer:

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.

The answer is:  

Example Question #9 : Using E

Simplify:  

Possible Answers:

Correct answer:

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.

Simplify the quadratic equation.

The answers are:  

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