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I. Linear Growth:
Suppose that the town has a fixed increase in population growth number of population increase each year.

Choose the amount of population growth each year = 200
(Hint: Choose a whole number for your growth rate, rather than a percent.)

a) Fill in the following chart:

Year (t) Population (P)
t = 0
(2010) 1000

t = 1
(2011) 1000+200=1200
t = 2
(2012) 1000+400=1400
t = 3
(2013) 1000+600=1600
t = 6
(2016) 1000+1200=2200

b) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.

Answer:P=200t+1000
Show your work here: Using the slope intercept form, with slope=growth rate =200, intercept= initial population=1000

c) Use your equation in part b to approximate the population in the year 2025.

Answer:
Show your work here:

d) Use your equation in part b to approximate how many years it will take the population to reach 7000.

Answer:
Show your work here:

e) Graph this function in MS Excel by plotting the points found in your chart in part a. Label your axes with time on the x-axis and population on the y-axis. Copy and paste your graph here:

Believe it or not, you have done the hard part.
Because you have the variables (letters from equation) defined, you just need to plug in the numbers for each:

Year ( t in years from 2010) Population (P)
Formula: P=200t+1000

Part C: Use your equation in part b to approximate the population in the year 2025.

What are you looking to find? (time or population)
So how many years have past? 2025-2010 = ?
Where does this number fit (time or population) in order to find what you are looking for?

Part D:Use your equation in part b to approximate how many years it will take the population to reach 7000.

What variable are you given (time or population)?
Which variable are you trying to find (time or population)?

Part E:Graph this function in MS Excel by plotting the points found in your chart in part a. Label your axes with time on the x-axis and population on the y-axis. Copy and paste your graph here:

Use time on the horizontal axis (x-axis) and population on the vertical axis (y-axis).
Your chart should look like this;
t / P=200t+1000 / P
0
1
2
3
t will be the x values and P will be the y values.

Hope this helps.
Melanie

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