Question

the original value of investment is $1400 anf the value incressed by 9%each year.write an exponential growtg function to modle this situation.then find the value of the investment after 25 years.

Answer 1

At year 0, the value of the investment is $1400.

After 1 year, we have to add 9% to the previous value, that is,

1400 + 1400*0.09 = 1400(1 + 0.09) = 1400(1.09) = 1526

After the second year, we have to add 9% to the previous value, that is,

1526 + 1526*0.09 = 1526(1 + 0.09) = 1526(1.09) = 1400(1.09)(1.09) = 1400(1.09)²

Following the same reasoning, after t years the function will be:

`y=1400(1.09)^t`

If t = 25, then:

`\begin{gathered} y=1400(1.09)^(25) \\ y=1400\cdot8.62308 \\ y=12072.31 \end{gathered}`

The value of the investment after 25 years will be $12,072.31