Question 9

9. [Maximum mark: 7]

A climate scientist is modelling an ice sheet as a rectangle.

She believes that the width ($x$ km) is increasing at a constant rate of 10 km per year and the length ($y$ km) is decreasing at a constant rate of 5 km per year.

The time, $t$, is measured in years, and the area, $A$, is measured in km$^2$.

When $t = 0$ then $x = 75$ and $y = 40$.

(a) Find $\frac{dA}{dt}$ when $t = 0$. [3]

(b) State, with justification, whether the area of the ice sheet is increasing or decreasing when $t = 0$. [1]

(c) Find the change in the area of the ice sheet between $t = 0$ and $t = 1$. [3]