Question

Person will get medal and fan if they help.
*NEED STEP BY STEP INSTRUCTIONS*

Joe deposits $1,500 in an account that pays 3% annual interest compounded continuously.
a. How much will Joe have in his account after 5 years?
b. How long will it take Joe to double his money? Use natural logarithms and explain your answer.

Answer 1

Use the formula:
A = Pe^(rt)
Where P is the amount you start with (1,500)
r is the rate (.05) in this case
and t is time (after 5 years so t = 5)
Can you solve question a from here?

Answer 2

Sorry the rate is (.03)

Answer 3

yes hold on

Answer 4

So this is the equation. 1500e^1.5?

Answer 5

e^.15
(.03 * 5) = .15

Answer 6

For a. i got 1500e^1.5 = 6722.53

Answer 7

Nope, you should have gotten 1742.75
You know what e is on your calculator right?

Answer 8

yeah.

Answer 9

I entered it like this into the calculator
1500e^(.03*5)

Answer 10

Ok now i got it. so it is 1742.75

Answer 11

it's like 1742.751364 (I don't know how much you need to round).

Answer 12

Its just to the tenth. now can you help me with part b? That is the harder part

Answer 13

Sure

Answer 14

This time we know what we need to get to double our money. 1500 * 2 = 3000
So put 3000 in for A in the equation we used before
3000 = 1500e(.03t) What we don't know is time. So we will solve for it.

3000 / 1500 = e^.03t
2 = e^.03t Now take the natural logarithm ON BOTH SIDES to get rid of e

ln(2) = ln(e)^.03t

This is important because ln(e) = 1 !!!!

ln(2) = .03t
ln(2) / 3 = t
t = 23.1 years
Understand?

Answer 15

The first part should read 3000 = 1500e^(.03t) I forgot to raise e to the power, but the rest is correct.

Answer 16

THANK YOU SO MUCH!

Answer 17

No probs! Anytime :)