Question

Suppose $5000 is invested at 7% interest compounded continuously. How long will it take for the investment to triple? Use the model a(t) = Pe^rt

Answer 1

\[A(t) = Pe ^{rt}\]

Answer 2

Good. That's the Amount formula for continuous compounding.

What does the verb "tiple" mean?

Answer 3

How do I find t

Answer 4

Again, please explain the meaning of "triple."

Answer 5

A(t)=5000*e^7%*t

Answer 6

triple = x3?

Answer 7

x3 of 5000?

Answer 8

3x, actually. In this problem, what "triples?"

Answer 9

the investment of $5,000?

Answer 10

Yes. if $5000 triples in value, what's the new value of your investment?

Answer 11

$15,000

Answer 12

Right. So, in the equation\[A=Pe ^{rt}, A has what\]

Answer 13

A(t)=$15,000

Answer 14

A has what value? P has what value?

Note that r should not be expressed as a percentage (7%), but as a decimal fraction.

Write the equation again, including the values of A, P and r.