Solve the Problem $P$ (In Decimal Form) at a Depth Of $x$

Multiple Choice

Solve the problem.
-Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light $P$ (in decimal form) at a depth of $x$ meters is given by $P = e ^ { - k x }$ , where $k$ is a constant related to the clarity and other physical properties of the water. The model for a particular lake is $P = e ^ { - 0.1284 x }$ . Determine the depth at which the light intensity is $80 \%$ of the value from the surface for this lake. Round to the nearest tenth of a meter.

A) $0.8 \mathrm {~m}$
B) $34.1 \mathrm {~m}$
C) $1.7 \mathrm {~m}$
D) $16.2 \mathrm {~m}$