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)0.75 1.5 3 6 12 24

Cheyanne Leigh

Cheyanne Leigh

Answered question

2021-06-09

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)0.75 1.5 3 6 12 24

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-06-10Added 99 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 2.
The recursive rule is f(0)=a and f(n)=b*f(n-1) with a the initial value (at n=0) and b is the growth factor (or decay factor if b<0).
Since a=0.75 and b=2 we then obtain the recursive rule: f(0)=0.75
f(n)=1/2f(n1)

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