Question

At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?

Answer 1

The correct format of the question is

At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people.
`P = 400 ( 1.2 )^ t` Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?

(A) 291

(B) 691

(C) 1040

(D) 1440

Answer:

The increase in the population at the end of 2009 is 291 people

Explanation:

We are given the equation as
`P = 400 ( 1.2 )^ t`

where

P = No of People

t= No of Years

it is given that in the year 2006 the population is 400

this will only happen when we take t= 0

so for

Year value of t

2006- t = 0

2007- t = 1

2008- t = 2

2009 t = 3

No of people in 2009 will be

`P = 400(1.2)^3`

= 400*1.728

P = 691.2

Since the equation represents no of people so it can't be in decimals, Therefore the population will be 691

Increase = P(2009) - P(2006)

= 691 - 400

= 291

The increase in the population at the end of 2009 is 291 people.