Consider the chemical reaction model described below. dy = ky² dt %3! Rate of change of y is propor- the square tional to of y. Use the chemical reaction model to find the amount y (in grams) as a function of time t (in hours). y = 90 grams when t = 0; y = 12 grams when t = 1

a) If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s2 = r3 − 60. ds/dr= ________ Interpret your answer to part (a) as a rate of change. b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 2. [Hint: Differentiate the original equation with respect to s.] dr/ds=___________ Interpret your answer to part (b) as a rate of change.

SSx = 172.5 = 80.6, and E[(X-My) (Y-Mx] = 95.33, r=