Previous Problem ListNext (1 point) Let P =f() = 1000( 1.025)\' be the populatio

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Previous Problem ListNext (1 point) Let P =f() = 1000( 1.025)' be the population of a community in year r. (a) Evaluate f(0) = | 1000 (b) Evaluate 10)= 1280.086 (c) Which of these statements correcty explains the practical meaning of the vilue you tound for GO) in par (o)? (elect al th (retain at least 3 decimal places) apply if more than one is correct) A. The initial population of the community B. How many years it takes for the population to reach 10,000 people. C. How much the population will increase in 10 years. D. The growth rate per decade of the population. E. How long it will take for the population to increase by 10 people. F. What the population will be in 10 years G. None of the above (d) If the percentage growth rate remains constant, approximately when will the popuiation reach 2300 people? In 34 years (round to the nearest whole year. Solution: Note: You can earn partial credit on this problem CorrectAnswers

Explanation / Answer

f(t) = 1000*(1.025)t

(a) f(0) = 1000*(1.025)0 => 1000

(b) f(10) = 1000*(1.025)10 => 1280.08454

(c) f(10) means what the population will be after 10 years.

(d) Given that f(t) = 2300 and corresponding 't' needs to be find

2300 = 1000*(1.025)t

take ln both sides

(ln 2.3)/(ln 1.025) = t

t = 33.7311 = rounded off to 34 years

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