Question

An initial investment of $350 is worth $429.20 after 6 years of continuous compounding. Find the annual interest rate. @freckles

Answer 1

\[A=A_0e^{rt}\]

Answer 2

is the formula for compounded continuously

Answer 3

You are given that A is 429.2 and A_0 is 350
and t is 6

Answer 4

They want you to solve for r

Answer 5

Ok so if i plug that into a graphing calc it will give me the answer?

Answer 6

you mean have it solve it for you?

Answer 7

You can solve for r yourself.
And use the calculator to give you an approximation for the the exact value you get for r

Answer 8

Ok

Answer 9

like this:
\[\text{ solving for } r \\ A=A_0e^{rt} \\ \text{ first step: divide both sides by } A_0 \\ \frac{A}{A_0}=e^{rt} \\ \text{ second step: Take } \ln ( ) \text{ on both sides } \\ \ln(\frac{A}{A_0})=\ln(e^{rt}) \\ \ln(\frac{A}{A_0})=rt \ln(e) \text{ by power rule for } \log \\ \ln(\frac{A}{A_0})=rt (1) \text{ since } \ln(e)=1 \\ \ln(\frac{A}{A_0})=rt \]
There is one last step to isolate r.
I will let you guess what that step is.

Answer 10

I got x= 0.034

Answer 11

sounds great
and your x is my r
where our x (or r) means the annual interest rate

Answer 12

you can write as a percent if you move the decimal over 2 places to the right
and put a percent sign

Answer 13

So 34%