Question

I'm using the equation A=Pe^rt. A=385.4 P=300 . t= 10 How do you find r? (please show all steps typed out!) Thanks!

Answer 1

Ah solving for r

Answer 2

\[A= Pe^{rt}\] this requires logarithms do you know it?

Answer 3

I guess first lets divide both sides by P \[\frac{ A }{ P } = e^{rt}\]

Answer 4

Now you can take the natural logarithm of both sides to cancel out the e, use the following rule \[\ln(e^x) = x\]

Answer 5

Ok I'm still kinda confused, can you please use the numbers that I have listed above? I'm trying to solve a couple problems similar to the one that is given.

Answer 6

Well I like to do the algebra before plugging in the numbers since it's more clearer, so have you used the rule I have showed you? See if you can apply it, and then we'll worry about the numbers after

Answer 7

You can check out the natural logarithm here as well http://www.rapidtables.com/math/algebra/Ln.htm

Answer 8

ok so I have 385.4=300e^r10. I then divided both sides by 300 which gave me 1.2846=e^r10. I then know I have to put ln on both sides to get rid of the 'e' on the one side so I should end up with ln(1.2846)=r10. (hope I did that right!) But this is where I get confused on what to do next.

Answer 9

do you have a calculator ?

Answer 10

yep!

Answer 11

use ur calculator and find the value of ln(1.2846)

Answer 12

Nice! You're doing really well, we just now have to divide by 10 \[\ln(\frac{ A }{ P }) = rt \implies \ln(\frac{ A }{ P }) \times \frac{ 1 }{ t } = r\] plugging in the numbers we have \[r = \ln \left( \frac{ 385.4 }{300 } \right) \times \frac{ 1 }{ 10 }\] you can use a calculator for this

Answer 13

OH! that was easy. I feel so dumb! :) So I should get 0.02504473858... This would be what r is correct?

Answer 14

Sounds good!

Answer 15

THANKS SO MUCH!!!!

Answer 16

Np