# exponential function

• Mar 12th 2008, 06:40 AM
mt_lapin
exponential function
A person invests \$7000 at 10% interest compounded annually. Let $f(t)$ be the value (in dollars) of the account at t years after he/she has deposited the \$7000.

a. Find an equation of f.

My answer: $f(t)=7000(1.10)^t$

b. What is the base b of your model $f(t)=ab^t$? What does it mean in this situation?

My answer: 1.10; the account balance increases by 10% each year.

c. What is the coefficient a of $f(t)=ab^t$? What does it mean in this situation?

My answer: 7000; the initial amount invested was \$7000.

d. What will be the account's value in 10 years? Explain why the value has more than doubled, even though the investment earned 10% for 10 years.

My answer: For the first part I got \$18156. But what would be the explanation? That I don't get...
• Mar 13th 2008, 12:55 AM
CaptainBlack
Quote:

Originally Posted by mt_lapin
A person invests \$7000 at 10% interest compounded annually. Let $f(t)$ be the value (in dollars) of the account at t years after he/she has deposited the \$7000.

a. Find an equation of f.

My answer: $f(t)=7000(1.10)^t$

b. What is the base b of your model $f(t)=ab^t$? What does it mean in this situation?

My answer: 1.10; the account balance increases by 10% each year.

c. What is the coefficient a of $f(t)=ab^t$? What does it mean in this situation?

My answer: 7000; the initial amount invested was \$7000.

d. What will be the account's value in 10 years? Explain why the value has more than doubled, even though the investment earned 10% for 10 years.

My answer: For the first part I got \$18156. But what would be the explanation? That I don't get...

Because the balance is compounded annualy you are earning interest on the interest paid in earlier years. So while the interest on the original sum over 10 years is \$7000 the account balance has more than doubled because of this interest on interest.

RonL