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tatiyna
1 year ago
14

In 2003 a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly.How m

uch 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 of 2000?Find the equation for the population, P, of the town t years after 2000.Using your equation predict the population of the town in 2014
Mathematics
1 answer:
sergiy2304 [10]1 year ago
3 0

We will have the following:

First, we will have that the population change by:

\Delta P=2134-1431\Rightarrow\Delta P=703

So, the population changed by 703 people.

It took the follwoing number of years to change from 1431 to 2134:

\Delta y=2007-2003\Rightarrow\Delta y=4

So, it took 4 years to changes from 1431 to 2134.

m=\frac{2134-1431}{2007-2003}\Rightarrow m=175.75

The average population growth per year is of 175.75 people per year.

The population in 2000 would have been:

P_{2000}=\frac{2000\cdot1431}{2003}\Rightarrow P_{2000}=1428.856715\ldots

\Rightarrow P_{2000}\approx1429

So, the population in 2000 would have been approximately 1429 people.

We will have that the equation for the population would be:

P=(\frac{2134-1431}{2007-2003})t+1429\Rightarrow P=\frac{703}{4}t+1429

So, the equation would be:

P=175.75t+1429

Now, we predict the number of people of the town in 2014:

P_{2014}=175.75(14)+1429\Rightarrow P_{2014}=3889.5

\Rightarrow P_{2014}\approx3890

So, there will be approximately 3890 people of the town in 2014.

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