Question

The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t² + 3 and w = t² - t + 2, then the rate of change of W with respect to t at t = 1 is ______ 

Options

• 1

• 13

• 5

• 8

Answer 1

The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t² + 3 and w = t² - t + 2, then the rate of change of W with respect to t at t = 1 is 13.

Explanation:

W = nw, n = 2t² + 3 and w = t² - t + 2

∴ `(dW)/dt = w(dn)/dt + n(dw)/dt,` where `(dn)/dt = 4t, (dW)/dt = 2t - 1` 

At t = 1,

n = 5, w = 2, `(dn)/dt = 4, (dW)/dt = 1`

∴ `((dW)/dt)_{(t = 1)} = 2(4) + 5(1) = 13`