Question

(4) (You must show all your work). Answer the following (independent) questions. (a) The approximate temperature T of the skin in terms of the temperature T, of the environment is given by T = 32.8 + 0.27(T,-20) where T and T, are in degree Celsius. Find the rate of change of T with respect to T (b) The value V of a certain machine after t years have elapsed is given by V = 120, 00-15, 50t where 0 t=47 6, How fast is V changing with respect to t when t = 2, and t A manufacturer has determined that for his product, 324 5 19 (5) (You must show all your work). the daily average cost (in hundreds of dollars) is given by V+35 18 (a) As daily production increases, the average cost approaches a constant amount. What is that amount? (b) Determine the manufacturer's marginal cost when 17 units are produced per day (e) The manufacturer determines that if production (and sales) were increased to 18 units per day, revenue would increase by $275. Should this move be made? Why? nomic analysis is the consumption function, C f(I). It expresses the relationship between the total income I and the total national consumption C. The marginal propensity to consume is defined as the rate of change of consumption with respect to income, ie. (6) (You must show all your work). A function that plays an important role in eco- dC Marginal propensity to consume = If we assume that the difference between income I and consumption C is savings S, then we define the marginal propensity to save as: 1 - Marginal propensity to consume Marginal propensity to save Suppose that a country's consumption function is given be 9v1 + 0.9「-0.31 where C and I are expressed in billions of dollars. (a) Find the marginal propensity to save when income is 25 billions. (b) Determine the relative rate of change of C with respect to I when income in 25 billions. (Hint: relative rate of change of a function f is f(x)/f(x).)

Answer 1