Thursday, September 22, 2011

Related rate-calculus~ HELP?

1.Animal psychologists have determined experimentally that the weight W and the surface area S of a typical horse are related by the empirical equation S=0.1W^(2/3). How fast is the surface area of a horse increasing at a time when the horse weights 350Kg and is gaining weight at the rate of 200kg/yr?

2. The revenueR a company receives is a function of the weekly sales x. also, the sales level x is a function of the weekly advertising expenditures A, and A in turn is a varying function of t, time.

a) Rate of change of revenue with respect to advertising expenditures

b)time rate of change of advertising expenditures

c)Marginal revenue

d)Rate of change of sales with respect to advertising expenditures.

Write a type of chain rule that expresses the time rate of change of revenue, dR/dt in term of three of the derivatives described above.

Help me! Thanks:)Related rate-calculus~ HELP?
s = 0.1 w^(2/3)

so s' = (2/3) 0.1 w^(-1/3) w'

s ' = (2/3) 0.1 350^(-1/3) 200 = 1.892 units/year

R = f(x); x = g(A), A=h(t)

dR/dt = f' g' h'

= marginal revenue * rate of change of sales wrt adverising * time rate of change of advertising expenditures
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