Question

Solve.The value of a particular investment follows a pattern of exponential grown. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential grown model $6400{e}^{0.047t}$How much did you initially invest in the account.

Answer 1

We know that the value of the investment t years after 2000 is given by the model:

$A=6400e^{0.047t}$

If we want to know how much did he initially invested, we replace the value t=0 on the model given (as zero years passed when he invested). This is:

$\begin{gathered} A(0)=6400e^{(0.047)(0)} \\ =6400e^0 \\ =6400(1) \\ =6400 \end{gathered}$

And thus, you initially invested in the account $6400.