two equation multiple? replace t value 8 then divided by 8?

Question

During the period 1992-2000 the number C (in million)of people participating in cross country skiing and the number S (in million) of people participating in snowboarding can be modeled by
C = 0.067 t^3 - 0.107 t^2 + 0.27 t + 3.5
S = 0.416 t + 1.24
Where t is the number of years since 1992.
a. Write an equation that model the total number of people T (in millions ) participating in cross country skiing and snowboarding as a function of the number of years since 1992.
b. Find the total participating in these activities in 1992 and 2000.
c. What was the average rate of change in total participation from 1992 to 2000 ?
Explain how you found this rate.

Answer 1

Hi Andrew.

 

The first thing I want to mention is how t is defined. t = # of years since 1992, meaning at 1992, t = 0.

 

t = 1, year is 1993.

t = 2, year is 1994... and so on.

 

a) The total people cross country skiing and snowboarding is just C + S.

 

T = C + S = 0.067 t^3 - 0.107 t^2 + 0.27 t + 3.5 + 0.416 t + 1.24

 

T = 0.067t^3 - 0.107t^2 + 0.686t + 4.74

 

b) Total people participating in 1992 refers to t = 0. Total people in 2000 refers to t = 8.

 

T(0) = 1.24

T(8) = 0.067(8)^3 - 0.107(8)^2 + 0.686(8) + 4.74

       = 37.684 million people.

 

c) The average rate of change in participation will be:

 

[f(8) - f(0)] / [8 - 0]

 

This will give the slope of the line going from (0, 1.24) to (8, 37.684), which will be average rate of growth between those two time points.

 

(37.684 - 1.24) / (8-0) = 4.555 million people/ year.

 

This means that, on average, an 4.555 million people began participating in this sport every year for 8 years.

 

Hope this helps.