The number of citizens in a town is growing according to a linear growth model. The initial population in week 0 was P_0=124 and the population after 18 months is P_ (18) = 184. Write an explicit formula for the number of citizens in the town depending on the month.

After how many months will the population reach 1000?

Question

Reagan Meyer

Mathematics

30 May, 20:32

The number of citizens in a town is growing according to a linear growth model. The initial population in week 0 was P_0=124 and the population after 18 months is P_ (18) = 184. Write an explicit formula for the number of citizens in the town depending on the month.

After how many months will the population reach 1000?

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Answers (1)

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Jared Payne · Answer 1

184 - 124 = 60

so it has grown by 60 in 18 months. That is 3 1/3 per month.

so Number of citizens depending on month is 124 + (1 1/3) n

or 124 + 4n/3:

At population 1000:-

124 + 4n/3 = 1000

4n/3 = 1000-124

n = (1000-124) * 3/4 = 657 months