exponential growth & decay\n1. vanessa invested $2,500 into an account that will increase in value by 3.5%…
exponential growth & decay\n1. 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
Explanation:
Step1: Write the exponential - growth formula
The general form of an exponential - growth formula is $A(t)=P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. Given that $P = 2500$, $r=0.035$ (since $3.5%=0.035$), the exponential function is $A(t)=2500(1 + 0.035)^t=2500(1.035)^t$.
Step2: Calculate the value of the investment after 20 years
Substitute $t = 20$ into the function $A(t)$. So, $A(20)=2500\times(1.035)^{20}$. First, calculate $(1.035)^{20}$. Using a calculator, $(1.035)^{20}\approx1.989788$. Then, $A(20)=2500\times1.989788 = 4974.47$.
Answer:
The exponential function is $A(t)=2500(1.035)^t$, and the value of the investment after 20 years is $$4974.47$.