Question

Daniel invested money in an account where interest is compounded every year. He made no withdrawals or deposits.The function A(t) = 645(1+0.06)^t represents the amount of money in the account after t years. How much money did Daniel originally invest?

Answer 1

An exponential growth can be modeled with the function

`\begin{gathered} y=I(1+r)^t \\ \text{where} \\ I\text{ is the initial value} \\ r\text{ is the rate} \\ t\text{ is the time} \end{gathered}`

The given function that represents the amount of money in the account after t years is

`\begin{gathered} A(t)=645(1+0.06)^t \\ \\ \text{where we can say that} \\ I=645 \\ r=0.06 \end{gathered}`

Since the initial value is 645, we can therefore say that the original amount of money Daniel invested is $645.