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# 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)96 54 48 24 12 6 3 ​

Exponential models
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asked 2021-06-10
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)96 54 48 24 12 6 3 ​

## Answers (1)

2021-06-11
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 1/2.
The recursive rule is f(0)=a and $$\displaystyle{f{{\left({n}\right)}}}={b}\cdot{f{{\left({n}-{1}\right)}}}$$ with a the initial value (at n=0) and b is the growth factor (or decay factor if b
Since a=92 and $$\displaystyle{b}=\frac{{1}}{{2}}$$ we then obtain the recursive rule: f(0)=96
$$\displaystyle{f{{\left({n}\right)}}}=\frac{{1}}{{2}}\cdot{f{{\left({n}-{1}\right)}}}$$

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