An exponential function is of the form y = ab^{x} where a represents the initial amount, b represents the common growth/decay factor, and x represents the time.

20 represents the initial amount or the number of rabbits when it was first counted, and 1.104

represents the common growth factor, b.

When x = 50, the value of p(x) is  y = 20(1.014)^{50} \approx 40

When x = 100, the value of p(x) is y= 20(1.014)^{100} \approx 80

The average rate can be calculated by the formula \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Plugging in (50, 40) as (x_{1}, y_{1}) and (100,80) as (x_{2},y_{2}) we get the average rate of change as \frac{80-40}{100-50} = \frac{40}{50} = 0.8.

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ALGEBRA I

Jun 12, 2018 ... Score 1: The student wrote one correct explanation. 33 A population of rabbits in a lab, p(x), can be modeled by the function p(x) 20(1.014)x, ...

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