The number of Mosquitos (M) that end up in a room is a function of how far the w

Question

The number of Mosquitos (M) that end up in a room is a function of how far the window is open (W, in square centimeters) according to M(W) = 5W+2. The number of bites (B) depends on the number of mosquitos according to B(M) = 0.5M. The question is to find the derivative of B as a function of W. i) What would be the "inside" function? ii) What would be the "outside" function? iii) Use the chain rule to compute this derivative. iv) Given your answers to i and ii, what would be the composition function that gives B(W) ? v) Compute B'(W) vi) compare answers to iii and v vii) Concept question: Without referring to the specific derivative computed, what do we learn from the derivative of B with respect to W in terms of bites and window openings.

Explanation / Answer

M = 5W + 2

B(M) = .5M

goal: find derivative of B as a function of W

4. B(W) means plug M into B: B(5W + 2) = .5(5W + 2) = 2.5W + 1

5. B ' (W) = 2.5

6. (iii) and (v) get the same answer. This is computing the derivative by two different methods.

7. B = # of mosquito bites; W = how far the window is open

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