long as the pollution remains in the lake
\[
f(t)=8\left(1-e^{-0.5 t}\right), g(t)=0.7 t
\]
a. How much pollution is in the lake after 14 hours?
The amount of pollution that remains in the lake after 14 hours is gallons
(Do not round until the final answer. Then round to the nearest hundredth as needed)
Answer
Rounding to the nearest hundredth, the final answer is \(\boxed{7.99}\) gallons of pollution in the lake after 14 hours.
Step 1 ：We are given the function for the amount of pollution in the lake as \(f(t)=8(1-e^{-0.5 t})\), where \(t\) is the time in hours.
Step 2 ：We need to find the amount of pollution in the lake after 14 hours, so we substitute \(t=14\) into the function.
Step 3 ：Calculating \(f(14)=8(1-e^{-0.5 * 14})\) gives us the amount of pollution in the lake after 14 hours.
Step 4 ：The result is approximately 7.992704944275564 gallons of pollution.
Step 5 ：Rounding to the nearest hundredth, the final answer is \(\boxed{7.99}\) gallons of pollution in the lake after 14 hours.
