Question

Vanessa invested $2,500 into an account that will increase in value by 3.5% each year. Write an exponential function to model this situation, then find the value of the investment after 20 years.

Answer 1

An exponential function is  $F = P (1+i)^{t}$. $4975 is the value of the investment after 20 years, if Vanessa invested $2500 that will increase in value by 3.5% each year.

Step-by-step explanation:

The given is,

                    Vanessa invested $2,500

                    Increase in value by 3.5% each year

Step:1

             Formula to calculate the future value is,

                                      $F = P (1+i)^{t}$.............................(1)

           Where, F - Future worth of the investment

                       P - Initial investment

                        i - Rate of increase

                         t - Time taken

        From given values,

                    P = $2500

                     i = 3.5%

                  t = 20 years

       Equation (1) becomes,

                                $F = 2500 (1+0.035)^{20}$               ( $i=\frac{3.5}{100} = 0.035$ )

                                    $= 2500 (1.035)^{20}$

                                    = (2500 × 1.989788)

                                    = 4974.4721

                                    ≅ $4975

                                F = $4975

Result:

             An exponential function is  $F = P (1+i)^{t}$. $4975 is the value of the investment after 20 years, if Vanessa invested $2500 that will increase in value by 3.5% each year.