Question

In 1960, the population of a town was `13` thousand people. Over the course of the next 50 years, the town grew at a rate of 30 people per year. Hint: let t=0 be 1960, and t=1 be 1961, etc. A) Assuming this continues, what is the population predicted to be in `2040`? B) Set up and solve the equation to find in which year the population will reach `16` thousand. Give your answer in a form like 1980 or 1994.A) peopleB)

Answer 1

Given:

In 1960, the population of a town was 13000 people.

Over the course of the next 50 years, the town grew at a rate of 30 people per year.

let t=0 be 1960, and t=1 be 1961

So, the population will increase by a constant number each year.

The equation to find the population will be as follows:

`p=30t+13000`

A) Assuming this continues, what is the population predicted to be in `2040`?

So, t = 2040 - 1960 = 80

Substitute t = 180

`p=30*80+13000=15400`

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B) Set up and solve the equation to find in which year the population will reach `16` thousand

Now, we will find the number of years the population will reach 16000

So, substitute p = 16000 then solve for (t)

`\begin{gathered} 30t+13000=16000 \\ 30t=16000-13000 \\ 30t=3000 \\ t=(3000)/(30)=100 \end{gathered}`

So, the year will be = 1960 + 100 = 2060

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So, the answer will be:

(A) = 15400 people

(B) 2060