The following functions give the population of three towns in terms of the numbe

Question

The following functions give the population of three towns in terms of the number of years, t, since 1995. Use this information to answer the following questions. Let L represent the population of Linwood: L-6500(1.18) Let N represent the population of Northfield: N = 8440(1.04)' Let S represent the population of Somers Point: S 11097(0.93) 0 a. In which town(s), if any, is the population increasing? (Select all that apply) Somers Point Linwood Northfield b. In which town(s), if any, is the population decreasing? (Select all that apply.) Linwood Somers Point Northfield h town experienced the largest I-year percent change of the population with respect to the number of years since 19951 Linwood What is this 1-year percent change? 18 % . Preview d. Which town had the largest population in the year 2000? Linwood e. In what year did the town of Somers Point have a population of 9270 people? Preview

Explanation / Answer

e) somers population is

S = 11097 ( 0.93)^t

plugging S = 9270

9270 = 11097(0.93)^t

9270 / 11097 = (0.93)^t

ln (9270/11097) = t ln (0.93)

t = ln (9270/11097) / ln (0.93)

t = 2.48

so, somers population will be 9270 people in the year 1998

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