Please show all work, all information needed is already provided! Thanks 4. A ce

Question

Please show all work, all information needed is already provided! Thanks

4. A certain apartment building, which you don’t want to live in, opened in 1995. In 1997, the number of mice infesting that building was 15. In 2002, there were 1242 mice. Let M represent the number of mice in years since 1995.

Find the equation that models M as a linear function of t.

Write M as an exponential function of t. What are the parameters of interest and what do they tell us about the growth in the number of mice over time?

What is the predicted number of mice in the building in 2013 based on the linear model? What about with the exponential model? If, in 2013, the actual number of mice observed turns out to be 20,500,000, calculate residual values to determine which model seems to be a more reliable predictor of the data. Explain how you know which model is more reliable.

Explanation / Answer

First taking linear model

Let say M = a+ bt [ where t = year number - 1995]

so 15 = a + 2b...(i)

1242 = a + 7b ...(ii)

b = 245.4

a = -475.8

M = 245.4 t - 475.8

so by putting t = ( 2013 - 1995) = 18

so Mice population at the 2003 = M(18) = 245.4 * 18 - 475.8 = 3941.4

But Actual M (2013) = 20500000

Residual = 20500000 - 3941.4 = 20496058.6 [ so much high]

Now Exponential model .

M = a ebt

so at t = 2 ; M = 15

so 15 = a * e2b...(i)

and at t =7; M = 1242

so 1242 = a * e7b...(ii)

1242/15 = e5b

b = 0.883

so by putting value in any equation

a = 2.563

so M = 2.563 e0.883x

so Now taking t = 2013 - 1995 = 18

M(18) = 2.563 e0.883 * 18 = 20484487

so Residual = 20,500,000 - 20484487 = 15513 ( seems good)

so we can see that there is very small residual in exponential model with respect to the linear model so we can say that exponential model is more reliable in this case.

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