Answer
$$
\left( f(x)=5000, \quad r =8, \quad 9 \% \right)
$$
If $f(t)=5000$ is the rate of continuous money flow at an interest rate $r=0.09$ for $T=8$ years, then the present value is
$$
\begin{aligned} P &=\int_{0}^{T} f(x) e^{-rt}dt \\
&=\int_{0}^{8} 5000 e^{-0.09 t} d t \\
& \approx \$ 28,513.76 \end{aligned}
$$
Work Step by Step
$$
\left( f(x)=5000, \quad r =8, \quad 9 \% \right)
$$
If $f(t)$ is the rate of continuous money flow at an interest rate $r$ for $T$ years, then the present value is
$$
P=\int_{0}^{T} f(x) e^{-rt}dt.
$$
If $f(t)=5000$ is the rate of continuous money flow at an interest rate $r=0.09$ for $T=8$ years, then the present value is
$$
\begin{aligned} P &=\int_{0}^{T} f(x) e^{-rt}dt \\
&=\int_{0}^{8} 5000 e^{-0.09 t} d t \\
&=\left.\frac{5000}{-0.09} e^{-0.09 x}\right|_{0} ^{8} \\ &=\frac{-5000}{0.09} e^{-0.72}+\frac{5000}{0.09}\\
& \approx \$ 28,513.76 \end{aligned}
$$