An agricultural worker in Uganda is planting clover to increase the number of bees making their home in the region. There are 100 bees in the region naturally, and or every acre put under clover, 20 more bees are found in the region.
(a) Draw a graph of the total number, N(x), of bees as a function of x, the number of acres devoted to clover.
(b) Explain, both geometrically and algebraically, the shape of the graph of:
(i) The marginal rate of increase of the number of bees with acres of clover, N¨(x).
(ii) The average number of bees per acre of clover, N(x)∕x.