The size of the trunk diameter of a chestnut oak tree, d, in centimetres, can be modelled by the function d(t) = 9 In(0.254), t 25, where t is the age, in years, of the tree. (a) Find the size of the trunk diameter of a 10-year-old chestnut oak tree. (b) The size of the trunk diameter of a chestnut oak tree is 15 cm. Find its age. A chestnut onk tree can be harvested for wood when the size of its trunk diameter reaches 20 ст. (c) Find the age of the chestnut oak tree when it is old enough to be harvested for timber.

The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth. Y = -55.12 - 0.01535N - 0.00056N? + 3.946R Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre.) Now we consider the amount of growth Y as a function of the amount of plant biomass N already present. (a) First we assume that the rainfall is 80 millimeters, so R = 80. (1) Find a formula for the growth Y as a function of the amount N of plant biomass already present. kg/ha (ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms…