Question

QuestionEnter the exponential function using t (for time) as the independent variable to model the situation. Thenfind the value of the function after the given amount of time.A new savings account is opened with $400 and gains 3.5% yearly for 5 years.The exponential function that models the situation is y = MyAfter 5 years, the savings account has $

Answer 1

Since, it is an exponential function, thus this is a compound interest problem;

Where; the function is given as;

`\begin{gathered} A(t)=P(1+r)^t \\ \text{Where A(t)= amount in the savings account at a time t} \\ P=ca\text{ pital invested} \\ r=\text{rate } \\ t=\text{ time} \end{gathered}`

Thus, the function required is;

`\begin{gathered} A(t)=400(1+(3.5)/(100))^t \\ A(t)=400(1.035)^t \end{gathered}`
`\begin{gathered} y=400(1.035)^t \\ \text{Where t is the time} \end{gathered}`

After 5 years,

`\begin{gathered} A(5)=400(1.035)^5 \\ A(5)=400(1.1877) \\ A(5)=475.07 \end{gathered}`

The amount in the savings account after five years is $475.07