Show that an exponential model fits the data. Then write a recursive rule that models the data.n 0 1 2 3 4 5 f(n)162 54 18 6 2 2/3 ​

Chaya Galloway

Chaya Galloway

Answered question

2021-07-01

Show that an exponential model fits the data. Then write a recursive rule that models the data.
n012345f(n)16254186223

Answer & Explanation

Cullen

Cullen

Skilled2021-07-02Added 89 answers

The given function represents an exponential model if every consecutive value is the previus value multiplied by a costant b that is called the growth (decay) factor. We not then that this table represents an exponential model, because the decay factors is 13.
The recursive rule is f(0)=a and f(n)=bf(n1) with a the initial value (at n=0) and b is the growth factor (or decay factor if b<0).
Since a=162 and b=13 we then obtain the recursive rule: f(0)=162
f(n)=13f(n1)

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