Answer
the total mass above a depth of 100 cm is 178 g.
Work Step by Step
The density of sediment (in grams per cubic centimeter) at the bottom of Lake Coeur d’Alene, Idaho, is given by
$$
p(x)=p_{0}e^{0.0133x}
$$
where $x$ is the depth (in centimeters) and is the density at the
surface.
The total mass of a square-centimeter column of sediment above a depth of $h$ cm is given by:
$$
\int_{0}^{h}p( t) d t
$$
If $p_{0}=0.85$ g per cm$^3$,then the total mass above a depth of 100 cm. is given by:
$$
\begin{aligned}
\int_{0}^{h}p( t) d x & =\int_{0}^{100}p_{0}e^{0.0133x} d x\\
& =\int_{0}^{100} (0.85)e^{0.0133x} d x\\
&=\int_{0}^{100} 0.85 e^{0.0133 x}\left(\frac{1}{0.0133}\right) d x \\
&=\left.\frac{0.85}{0.0133} e^{0.0133 x}\right|_{0} ^{100} \\ &=\frac{0.85}{0.0133}\left(e^{1.33}-e^{0}\right) \\ & \approx 177.736
\end{aligned}
$$
So, the total mass above a depth of 100 cm is 178 g.
