Let P = f(t) = 1150(1.037)^t be the population of a community in year t. (a) Eva

Question

Let P = f(t) = 1150(1.037)^t be the population of a community in year t. (a) Evaluate f(0) = (b) Evaluate f(10) = (retain at least 3 decimal places) (c) Which of these statements correctly explains the practical meaning of the value you found for f(10) in part (b)? (select all that apply if more than one is correct) A. How many years it takes for the population to reach 10,000 people. B. The growth rate per decade of the population. C. How long it will take for the population to increase by 10 people. D. What the population will be in 10 years. E. How much the population will increase in 10 years. F. The initial population of the community. G. None of the above

Explanation / Answer

f(t) = 1150 (1.037)t where 't' is in years
a) f(0) = 1150 (1.037)0 = 1150
Population after 0 years i.e. at the beginning of time is = 1150
b) f(10) = 1150 (1.037)10 = 1150*1.43809495 = 1653.8092~= 1653.809

This means that the population after a time period of 10 years will be = 1653.809

c) Thus f(10) represents what the population will be in 10 years.
Hence the correct choice is D

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