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 = `2t^(2)+3` and `w=t^(2)-t+2`, then the rate of change of W with respect to t at t = 1, is

Options

A. 1
B. 13
C. 5
D. 8

Answer

B

Explanation

We have,
`W=nw, n=2t^(2)+3 and w=t^(2)-t+2`
`therefore (dV)/(dt)=(dn)/(dt)w+n(dw)/(dt),(dn)/(dt)=4t,(dW)/(dt)=2t-1`
At t=1, we get
`n=5,w=2, (dn)/(dt)=4, (dw)/(dt)=1`
Hence, `((dW)/(dt))_(t=1)=4xx2+5xx1=13`