Modeling linear function word problem. Fun!?
I think I figured this problem out but I wanted to see what other people might come up with for an answer, I do not know the answer the book does not have it in the answer key which makes it more challenging. here it is.
In 1998, the number of people (in millions) reporting arthritis was 43. The number of people (in millions) predicted to be reporting arthritis in 2020 is 60. Let y be the number of people (in millions) reporting arthritis in year x, where x= 0 represents 1998. (source: Arthritis foundation)
a. Write a linear equation that models the number of people (in millions) reporting arthritus in terms of the year x.
b. Use this equation to predict the number of people reporting arthritis in 2010. ( Round to the nearest million.)
Have fun! I'm interested to see what answers appear.
Tagged with: answer key • arthritis • Arthritis Foundation • arthritus • linear equation • models
Filed under: Arthritis Foundation
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<< Write a linear equation that models the number of people (in millions) reporting arthritis in terms of the year x. >>
You have two points given, i.e.,
(1998,43) and (2020,60)
and given the above two points, the slope can be determined (since the relationship has been premised to be linear)
m = slope = (60 – 43)/(2020 – 1998)
m = 0.7727
The linear equation is, therefore,
0.7727 = (y – 43)/(x – 1998)
0.7727(x – 1998) = y – 43
y = 43 + 0.7727(x – 1998) — this is your linear equation
<< Use this equation to predict the number of people reporting arthritis in 2010. ( Round to the nearest million.) >>
Substituting 2010 for "x" in the above derived linear equation,
y = 43 + 0.7727(2010 – 1998)
y = 43 + 9.3
y = 52.3 or rounding off to the nearest million,
y = 52,000,000 people
Hope this helps.
2020 – 1998 = 22 years
T1 = 43
T22 = 60
T22 = T1 + 21d
60 = 43 + 21d
21d = 17
d = 17/21
after x years = 43 + [(x – 1) × 17/21]
In 2010
2010 – 1998 = 12 years
= 43 + 11 × 17/21
= 51.90
——–