Question

I need help with solving this equation of an unequal base.

Answer 1

The first equation is A(t) = 39,145 (1+ .03/12) ^12(t)

Answer 2

A(t) = 10,000 and I have to solve for t, i just know I am doing something wrong and I know I am going to feel stupid when I have help to solve this.

Answer 3

\[A(t) = 39145 \times (1 + \frac{ 0.03 }{ 12 })^{12t}\]\[A(t) = 10000\]
\[10000 = 39145 \times (1 + \frac{ 0.03 }{ 12 })^{12t}\]\[\frac{ 10000 }{ 39145 } = (1 + \frac{ 0.03 }{ 12 })^{12t}\]\[\ln(\frac{ 10000 }{ 39145 }) = \ln((1 + \frac{ 0.03 }{ 12 })^{12t})\]\[\ln(\frac{ 10000 }{ 39145 }) = \ln(1 + \frac{ 0.03 }{ 12 }) \times 12t\]\[t = \frac{ \ln(\frac{ 10000 }{ 39145 }) }{ \ln(1 + \frac{ 0.03 }{ 12 }) \times 12 } \approx -45.5464\]
I don't know were you got stuck, but i have provided how I'd do all the steps. Hopefully it might clarifies things for you :)

Answer 4

Note:

You can use any logaritm base you like. \[\ln, \log _{10}, \log _{3}, \log _{100}\]as long as you are using the same for both expressions the base won't matter.

I just happen to like ln ^^

Answer 5

Thank you so much, see as I said it is as simple as pie, but I didn't see it. I think I didn't remember that I was supposed to put logarithms into the problem and I just jumbled myself up. Thank you so much you were so much help :)