Question

Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.

Answer 1

Hello,

Explanation:

Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.

`P(t)=125*e^(0.035*t)\\a)\\P(2000)=125*e^(0.035*(2000-1990))=177.38...\\\\b)\\P'(t)=125*0.035*e^(0.035*t)\\\\c)\\\\P'(2000)=125*0.035*e^(0.035*(2000-1990))=6.2084...`