The "average rate of change" means how many new mice per year during those years.
How many are there at the end of the 2nd year ?
P(2) = 2,000(1.05)² = 2,205 mice
How many are there at the end of the 5th year ?
P(5) = 2,000(1.05 to the 5th power) = 2,552.6 mice
The average rate of change during those 3 years is (new mice in 3 years) / 3
That's (2552.6 - 2205) / 3 = **347.6 . **
To the nearest whole number, it's 348 mice per year ... Choice #2.
That's a lotta mice !
To find the growth of a population, calculate the change in population over a specific time period, and divide that by the number of years to find the average growth rate. For example, a population growing from 200 to 300 chipmunks over 2 years has an average growth rate of 50 chipmunks per year. Using the exponential growth formula can help analyze further growth predictions.
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