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

• A. $1$
• B. $13$
• C. $5$
• D. $8$

Answer 1

Answer: (B)

$13$

The weight $W$ of a certain stock of fish is given by

$n=2t^2+3$

At $t=1\Rightarrow n=5$

$\frac{dn}{dt}=4t$

$\Rightarrow {\left(\frac{dn}{dt}\right)}_{t=1}=4$

$w=t^2-t+2$

At $t=1\Rightarrow w=2$

$\frac{dw}{dt}=2t-1$

$\Rightarrow {\left(\frac{dw}{dt}\right)}_{t=1}=1$

We have $W=nw$

$\Rightarrow \frac{dW}{dt}=n\frac{dw}{dt}+w\frac{dn}{dt}$

$\Rightarrow {\left(\frac{dW}{dt}\right)}_{t=1}=5+8=13$

Hence, option 'B' is correct.