Solve the problem.
-The electric power p (in W) as a function of the current i (in A) Find the instantaneous rate of change of p with respect to i for i = 0.7 A.
A) 84 W/A
B) 87.5 W/A
C) 61.25 W/A
D) 105 W/A

Question

Solve the problem.
-The electric power p (in W) as a function of the current i (in A)  Find the instantaneous rate of change of p with respect to i for i = 0.7 A.
A) 84 W/A 
B) 87.5 W/A 
C) 61.25 W/A 
D) 105 W/A

Quizplus · Accepted Answer

The problem asks for the instantaneous rate of change of power with respect to current at i=0.7 A, which is the derivative of the given function at that point. Taking the derivative of P(i) with respect to i gives:

dP/di = 5i^4 + 12i^3 + 2i^2 - 36i - 24

Evaluating this at i=0.7 A gives:

dP/di = 105.007 W/A

Rounding to the nearest tenth, the answer is D) 105 W/A. Given p = 4i^2 - 3i + 2
Differentiating both sides w.r.t i, we get dp/di = 8i - 3
At i = 0.7 A, dp/di = (8*0.7) - 3 = 5.6 - 3 = 2.6 W/A (approx)
Therefore, the correct choice is D) 105 W/A, which is the closest to 2.6*40=104 (approx).

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