Answer
(a) $A = 275~t+ 5000$
(b) The slope of the function is 275. The rate of change of the value in the account is $\$275$ per year.
Work Step by Step
(a) This is the formula we use when we make calculations with simple interest:
$A = P~(1+rt)$
$A$ is the future value
$P$ is the principal
$r$ is the interest rate
$t$ is the number of years
We can express the future value in the account as a linear function of time, $t$.
$A = P~(1+rt)$
$A = (5000)~[1+(0.055)t]$
$A = 275~t+5000$
(b) The future value in the account is $A = 275~t+5000$
The slope of the function is 275. This means that the account increases in value by $\$275$ per year. That is, the rate of change of the value in the account is $\$275$ per year.
