Question

If $7500 is invested at an interest rate of 5% each year, what is the value of the investment in 4 years? Write an exponential function and solve.

Answer 1

An exponential function is:
`A(t) = P(1+r)^t`

Value of the investment in 4 years is, $9,116.29688

Explanation:

Using formula of an exponential function

`A(t) = P(1+r)^t` .....[1]

where

A(t) is the amount

P is the principal

r is the rate of interest in decimal

t is the time in years

As per the statement:

P = $7500

r = 5% = 0.05

t =4 years

then substitute these in [1] we get;

`A(4) = 7500(1+0.05)^4`

⇒
`A(4) = 7500(1.05)^4`

Simplify:

`A(4) = 7500 \cdot 1.21550625 = \$9,116.29688`

Therefore, the value of the investment in 4 years is, $9,116.29688

Answer 2

f(x)= 7500*(1+0.05)^4=9116,29