Sofia G.

asked • 05/04/15

Solve the word problem

A club has 288 members in 1997, 329 members in 1998, and 367 members in 1999. Find the rate of change in members per year. Round your answer to the nearest integer.

Stephanie M.

tutor
It's not clear whether you want a linear rate of change (like the slope of a line) or an exponential rate of change (like how fast a curve is getting steeper).
 
For the linear rate of change, you just want (change in y)/(change in x). Every time the year (x) changes by 1, the membership (y) changes by how many people, on average?
 
For the exponential rate of change, you'll be more interested in how quickly the membership is growing as a percent value. You'll want the ratio of one year to the previous year: 329/288 = what percent of growth? 367/329 = what percent of growth?
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05/05/15

Mark M.

Linear rate of change is not constant. Therefore it cannot be determined for the three years.
For exponential growth the rate is not constant. First year is is 1.142%, the second year it is 1.11%
 
The question is ambiguously worded.
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05/05/15

Jeff C.

tutor
Based on the simplicity of the problem statement, I assumed she was looking for the slope of a line. The more expert you are in a given subject, the more ambiguous a question can appear.
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06/28/24

1 Expert Answer

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Jeff C. answered • 06/28/24

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MS in Electrical Engineering With Years of Tutoring Experience
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The average rate of change is by definition the slope m of a line determined by two pairs of points.


m = (y2 - y1)/(x2 - x1)


The first two points are (1997, 288) and (1998,329). The second pair of points is (1998,329) and (1999,367).


The slope for the first pair of points is m1 = (329 - 288)/(1998-1997) = 41 per year

The slope for the second par of points is m2 = (367-329)/(1999-1998) = 38 per year

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