- [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 km².
When t = 0 then x = 75 and y = 40.
(a) Find 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]