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 $

Answers

Answer 1

Answer:

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

Where; the function is given as;

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

Thus, the function required is;

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

After 5 years,

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

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

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