Question

5400 dollars is placed in an account with an annual interest rate of 9%. To the

nearest tenth of a year, how long will it take for the account value to reach 15500
dollars?

Answer 1

12.2 years

Explanation:

To solve, use the exponential growth formula:

`A_t=A_0(1+r)^x`

where

`A_t` = Amount as a function of time ($15500)

`A_0` = Original amount ($5400)

`r` = rate (.09)

`x` = time in years

So,

`15500=5400(1+.09)^x\\15500((1)/(5400))=5400(1.09)^x((1)/(5400))\\2.87=1.09^x\\\log_(1.09)2.87=\log_(1.09)1.09^x`

Use the logarithmic rules that state
`\log_(a)a=1` and
`\log_(a)a^b=b\log_(a)a`:

So,

`\log_(1.09)2.87=x\\12.24\ years=x`