Answer
The total revenue in the first 4 years is $\$78,000$
Work Step by Step
We can find the total revenue in the first 4 years:
$\int_{0}^{4}9000~\sqrt{1+2t}~dt$
We can use substitution:
Let $u = 1+2t$
$\frac{du}{dt} = 2$
$dt = \frac{du}{2}$
When $t = 0$, $u = 1$
When $t = 4$, $u = 9$
We can find the total revenue in the first 4 years:
$\int_{0}^{4}9000~\sqrt{1+2t}~dt$
$=\int_{1}^{9}4500~\sqrt{u}~du$
$=(\frac{2}{3})(4500)~(u)^{3/2}~\vert_{1}^{9}$
$=(3000)~(9^{3/2}-1^{3/2})$
$=(3000)~(27-1)$
$=(3000)~(26)$
$=78,000$
The total revenue in the first 4 years is $\$78,000$
