The annual number of passengers going through Hartsfield-Jackson Atlanta Interna

Question

The annual number of passengers going through Hartsfield-Jackson Atlanta International Airport between 2000 and 2008 can be modeled as p(t) = -0.102t^3 + 1.39t^2 - 3.29t + 79.25 where output is measured in passengers and t is the number of years since 2000. Numerically estimate p(4) to the nearest thousand passengers. Interpret the result. At the end of 2004, the number of passengers going through Hartsfield-Jackson International Airport was by approximately per year. Calculate the percentage rate of change of p at t = 4. % per year. Interpret the result. At the end of 2004, the number of passengers going through Hartsfield-Jackson International Airport was by approximately % per year.

Explanation / Answer

given P(t)=-0.102t3+1.39t2-3.29t+79.5

differentiate with respect to t

P'(t)=-0.102*3t3-1+1.39*2t2-1-3.29*1+0

P'(t)=-0.306t2+2.78t-3.29

a) P'(4)=-0.306*42+2.78*4 -3.29

P'(4)=2.934 million passergers / year

increasing at P'(4)=2934000 passergers / year

b)P(4)=-0.102*43+1.39*42-3.29*4+79.5

P(4)=82.052million passengers

percentage rate of change =(P'(4)/P(4))*100

percentage rate of change =(2.934/82.052)*100

percentage rate of change =3.576%

INCREASING AT 3.576%

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