Math problem question ( Please help me)

Question

The data below illustrates Canada's median age as a relation to time.

Year Median Age

1911 23.8

1921 23.9

1931 24.7

1941 27

1951 27.7

1961 26.3

1971 26.2

1981 29.6

1991 33.5

2001 37.6

b.Find the algebraic model that best describes the data.

c. Using your equation, determine the average rate of change between:

i. 1950 to 1960

ii. 1980 to 2000

d. What will the instantaneous rate of change be in 2010?

e. Is Canada's median age increasing or decreasing? Suggest reasons why this is occurring?

Answer 1

If you plot the data you see that it is "kind of" linear:

The equation of this linear model can be found either using a manual method (which I can tell you about but it's quite messy) or by using a graphing calculator (like the TI-84) or a computer graphing tool like desmos.

In a TI-84, you put the data in a list and use the linear regression command. You'll find that the results are:

("A" = average age and "Y" = year): A(Y) = 0.128545Y - 223.405 however, the R² value for this is only 0.77 which is not terrible but really not that great.

Since you have the data already in your calculator, it's easy to do other modeling:

Using a quadratic the R² value improves to 0.89

Using a cubic the R² value improves to 0.95

Using a quartic the R² value improves to 0.96

The result of the quartic model is:

A(Y) = 7.4155x10^-7Y⁴ - 0.00574064Y³ + 16.6638Y² - 21496,6Y + 1.0398x10⁷

The other models (exponential, power, log, etc) don't provide very good R² values.

So, since I'm unsure exactly how you were taught to do this sort of problem and what type of model you are supposed to use, I'll just leave it at that. If you want to know more about any of these, message me back and I'll go into detail.

You can use these models to answer the other questions.