OpenStudy (abbles):

Solve for x. Write your answer to three decimal places.

1 year ago
OpenStudy (abbles):

\[(1000)(1.05)^3x = 3000\] The x should be part of the exponent after 3 !!!

1 year ago
OpenStudy (abbles):

My answer: 20.496 But I'm not sure it's right...

1 year ago
OpenStudy (jim_thompson5910):

Let's test that answer \[\Large 1000*1.05^{3x} = 3000\] \[\Large 1000*1.05^{3*20.496} = 3000\] \[\Large 1000*1.05^{61.488} = 3000\] \[\Large 1000*20.0857300355072 = 3000\] \[\Large 20085.7300355071 = 3000\] The last equation is false, so the first equation is false when x = 20.496 So you don't have the correct answer.

1 year ago
OpenStudy (abbles):

Mm I should have thought about checking it by plugging it in... would you mind going through the problem with me?

1 year ago
OpenStudy (jim_thompson5910):

Was your first step to divide both sides by 1000?

1 year ago
OpenStudy (abbles):

Yes. 1.05^3x = 3 Then I took the natural log of both sides... maybe that's where I went wrong? ln(1.05)(3x) = ln3

1 year ago
OpenStudy (jim_thompson5910):

\[\Large 1000*1.05^{3x} = 3000\] \[\Large 1.05^{3x} = 3\] \[\Large \ln(1.05^{3x}) = \ln(3)\] \[\Large 3x*\ln(1.05) = \ln(3)\] \[\Large x = \frac{\ln(3)}{3\ln(1.05)}\] \[\Large x = ???\]

1 year ago
OpenStudy (abbles):

I forgot the take the natural log of the right side! Ahh okay. Is the answer 7.5 ish?

1 year ago
OpenStudy (jim_thompson5910):

7.50569510180368 yes

1 year ago
OpenStudy (jim_thompson5910):

to three decimal places, that would be 7.506

1 year ago
OpenStudy (jim_thompson5910):

Using a calculator, 1000*1.05^(3*7.506) = 3000.13388728502 so that's close enough

1 year ago
OpenStudy (abbles):

Perfect! Thanks for going through the problem with me :) I see what I did wrong.

1 year ago
OpenStudy (jim_thompson5910):

you're welcome

1 year ago