Question

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

Exponential models
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asked 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

Expert Answers (1)

2021-06-10

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
\(f(n)=1/2*f(n-1)\)

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