- Difficulty
- Introductory
- Suggested time
- 2 min
- Marks
- 1
The definition of the derivative practice question 5
Biologists counted 2340 salmon spawning in a creek in 2016 and 1620 in 2024. Find the average rate of change of the count over that period: the slope of the line through the two data points.
Give the answer in salmon per year.
Between 2016 and 2024, did the count go up or down? Let the sign of your rate say so.
Slope is rise over run: the change in the count divided by the number of years that passed. Subtract in the same order, later minus earlier, on top and bottom.
An integer.
Theory UBC Math 100 §3.1Key results
Worked solution
Strategy
The average rate of change over an interval is the slope of the line through the two data points: change in count over change in time, with both differences taken in the same order.
Working
Later value minus earlier value, for the count and for the time.
The count fell, so the line slopes down and the rate is negative.
Answer
The answer is negative 90 salmon per year.
Check
Losing 90 a year for 8 years is 720 salmon, and 2340 − 720 = 1620, the 2024 count.
Where this goes wrong
Dropping the minus sign. The count fell from 2340 to 1620, so the rate is −90 salmon per year; +90 would describe a run that is growing.
Leans on
Slope of a line through two points, from Functions, graphs and inverses
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