Math Is Fun Forum

Hello, I need help with this formula

**Sorry that I edited this alot, it's my first time using latex.

Hello, I think the answer for
http://www.mathopolis.com/questions/q.php?id=589
Have a typo.
Q : 3 years ago you had $120 in the bank. You now have $192.
If the amount of money at the end of each year increases exponentially, then how much will you have in the bank after another 7 years?
(Assume that you do not deposit or withdraw any money)

A : Start with the formula y(t) = aekt
We know y(0) = 120
⇒ 120 = ae0
⇒ a = 120

We also know y(3) = 192
⇒ 192 = 120e3k
⇒ e3k = 192 ÷ 120 = 1.6
⇒ 3k = ln(1.6) = 0.470...
⇒ k =  0.470... ÷ 3 = 0.156668...

Now we know a and k, we can write the growth function y(t) = aekt explicitly as
y(t) = 120e0.156668t

Now, we can find how much money there will be in the bank after a further 6****(isn't this 7) years by replacing t with 10:

y(10) = 120e0.156668 × 10
= 120e1.56668
= 120 × 4.79071658...
= 574.89

You will have $574.89 in the bank after a further 7 years

Sorry if I was wrong, please explain.