Question

In 2003, a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly. Answer the questions below and to earn full credit show all work/calculations/thinking.How much did the population grow between the year 2003 and 2007?How long did it take the population to grow from 1431 people to 2134 people?What is the average population growth per year?What was the population in the year 2000?Find an equation for the population, P, of the town t years after 2000.Using your equation, predict the population of the town in 2014.

Answer 1

We know that the population in 2003 and 2007 is:

2003: 1431

2007: 2134

1. To know how much the population grow from 2003 to 2007, we need to subtract the population in 2003 from the population of 2007:

Growth = 2134 - 1431 = 703

2. It took (2007 - 2003) = 4 years for the population to grow from 1431 to 2134.

3. The average population growth per year can be calculated as:

Average = Growth / (# of years) = 703/4 = 175.75

4. Since it is a linear model, the growth rate is constant for all years. 3 years passed from 2000 to 2003, and the average growth per year is 175.75, so the population in the year 2000 is:

Population_2000 = Population_2003 - 3*Average

Population_2000 = 1431 - 3*175.75 = 903.75

To the nearest whole number, the population in the year 2000 was 904.

5. The linear model is:

`P(t)=m\cdot t+b`

Where P is the population of the town t years after 2000, m is the average growth per year and b is the population in the year 2000. Using our results:

`P(t)=175.75\cdot t+904`

6. For the year 2014 the value of t is 14. Then, using our linear model, the population is:

`P(14)=175.75\cdot14+904=3364.5\approx3365`

The population of the town in 2014 will be 3365.