Answer:
The snake is gaining weight at a rate 110.925 gram per year.
Step-by-step explanation:
Give that,
The weight of the snake is [tex]W= 439 x^3[/tex].
[tex]W= 439 x^3[/tex]
Differentiating with respect to t
[tex]\frac{dW}{dt}=493 \times3x^2\frac{dx}{dt}[/tex]
The snake is growing at the rate 0.3 meter per year. That is [tex]\frac{dx}{dt}=0.3[/tex] m per year.
Putting the value of [tex]\frac {dx}{dt}[/tex]
[tex]\therefore \frac{dW}{dt}=493 \times 3x^2\times 0.3[/tex]
The length of the snake is 0.5 meter. i.e x= 0.5
[tex]\therefore \frac{dW}{dt}|_{x=0.5}=493 \times 3(0.5)^2\times 0.3[/tex]
=110.925 gram per year
The snake is gaining weight at a rate 110.925 gram per year.
