Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

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

Answer 5

Was your first step to divide both sides by 1000?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

7.50569510180368

yes

Answer 10

to three decimal places, that would be 7.506

Answer 11

Using a calculator,

1000*1.05^(3*7.506) = 3000.13388728502

so that's close enough

Answer 12

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

Answer 13

you're welcome