Exercise 2 Page 222

Let's find the population of Clarksville in the years in the options. Let's start with option F. To use the model, we need the number of years since 1960. t=1974-1960=14Let's substitute this value in the quadratic model.

P(t)=-0.068t^2+7.85t+56

Substitute

t= 14

P( 14)=-0.068( 14^2)+7.85( 14)+56

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Evaluate right-hand side

CalcPowProd

Calculate power and product

P(14)=-13.328+109.9+56

AddTerms

Add terms

P(14)=152.572

Let's repeat the process for all options.

Option	Year	t	Expression	P(t)
F	1974	1974-1960= 14	-0.068( 14^2)+7.85( 14)+56	152.572
G	1977	1977-1960= 17	-0.068( 17^2)+7.85( 17)+56	169.798
H	1981	1981-1960= 21	-0.068( 21^2)+7.85( 21)+56	190.862
J	1983	1983-1960= 23	-0.068( 23^2)+7.85( 23)+56	200.578

We can see that according to this model it was 1983 when the population of Clarksville reached 200 000 people. The correct answer is J.