Answer
1 year -> 5200 dollars
2 years -> 5408 dollars
3 years -> 5624.32 dollars
4 years -> 5849.29 dollars
5 years -> 6083.26 dollars
6 years -> 6326.60 dollars
Work Step by Step
First one has to find the function that models the example. This uses an exponential function and its base is $f(x)=n\cdot r^x$ where $n$ is the initial value and $r$ is the growth rate. There is an initial investment of \$5000 dollars, so that corresponds to $n$. The interest rate is 4%, so the growth rate is 104% which is 1.04 in decimal form and it corresponds to $r$. Now the function can be described:
$f(t)=5000\cdot 1.04^t$
Now one only needs to calculate $f(1), f(2), f(3), f(4), f(5), and f(6) which corresponds to the investment after 1, 2, 3, 4, 5, and 6 years, respectively.
