Consider the United States census data from Section 1.1 of the text (Following f

Question

Consider the United States census data from Section 1.1 of the text (Following figure Table 1.1). Take t to be time in years, with origin 1790 (as in the text and in class). Model this population by an equation P(t) = P0*e^(kt) [LaTeX:P(t)=P0ekt] where the actual values at t = 10 and t = 20 are used to determine P0 [LaTeX:P0] and k. Express your answer also in the form P(t) = Q0e^(k1(t?10)) [P(t)=Q0ek1(t?10)] (P0,Q0,k,k1should be given as decimals.) Compare the value P(80) given by this formula with the actual value at t = 80 and the value given by the model in the text.

Explanation / Answer

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so we get

P(T)=[3.9013][E^(0.0306374T)].............ANSWER

WHAT DO YOU MEAN BY ?? HERE

Express your answer also in the form P(t) = Q0e^(k1(t?10)) [P(t)=Q0ek1(t?10)] (P0,Q0,k,k1 should be given as decimals.)

NOT CLEAR ...SO LEAVING IT ..

AT T=80 WE GET

P(80)=[3.9013][E^(0.0306374*80)]=45.254..........ANSWER

ACTUAL IS ....39

P(T)=P(0)*[E^(KT)]...........................1 AT T=10......P(10)= 5.3 5.3=P(0)[E^10K]...............................2 AT T=20.......P(20)=7.2 7.2=P(0)[E^20K]............................ EQN.3/EQN.2 GIVES ..... 7.2/5.3 = E^10K K=0.03063742 PUTTING IN 1 P(0)=3.90139

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