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Show that an exponential model fits the data. Then write a recursive rule that models the data.

Exponential models
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asked 2021-05-09
Show that an exponential model fits the data. Then write a recursive rule that models the data.

Answers (1)

2021-05-10
The given function represents an exponential model if every consecutive valueis the previous value multiplied hy a. constant bthat is called the growth (decay) factor. We note then that this table represents an exponential model, because the growth factor is 4.
The recursive rule is f(0)=a and f(n) = b*f(n—1) with a the initial value (at n = 0) and dis the growth factor (or decay factor is b < 0).
Since a = 2 and b= 4 we then obtain the recursive rule: f(0)=2
f(n)=4f(n-1)
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