Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given by . Find how long it will be before the oxygen level reaches its minimum.
E)none of the above

Question

Suppose that the oxygen level P (for purity) in a body of water t months after an oil spill is given by  . Find how long it will be before the oxygen level reaches its minimum. ​​
E)none of the above

Quizplus · Accepted Answer

To find the minimum of the function, we need to find the critical points. 
P(t) = 80e^(-0.2t) - 6t + 70 
P'(t) = -16e^(-0.2t) - 6 
To find the critical point, we need to solve P'(t) = 0: 
-16e^(-0.2t) - 6 = 0 
e^(-0.2t) = 3/8 
-0.2t = ln(3/8) 
t = -5ln(3/8) 
t ≈ 6.98 
Therefore, the oxygen level reaches its minimum value approximately 6.98 months after the oil spill. 
The answer is B, 11eb0d3b_9866_d6d4_9790_050db224f2c8_TB1243_11.

Suppose That the Oxygen Level P (For Purity) in a Body