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# Show that an exponential model fits the data. Then write a recursive rule that models the data. \begin{array}{|l|l|l|l|l|l|l|} \hline n & 0 & 1 & 2 &

Exponential models
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asked 2021-06-30

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

$$\begin{array}{|c|c|} \hline n & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline f(n) & 2 & 6 & 18 & 54 & 162 & 486 \\ \hline \end{array}$$

## Answers (1)

2021-07-01

The values of n are increasing by 1 and the values of $$f(n)$$ are increasing by a factor of 3 which means the datais exponential. The formula, will then be of the form $$f(n) = ab^n$$. The data point (0,2) means $$a=2$$.
Since the values of $$f(n)$$ are increasing by a factor of 3, $$b = 3$$. The exponential formula is then $$f(n) = 2(3)^n$$. A recursive rule for an exponential data set is of the form $$f(0) = a$$ and $$f(n) = b\cdot f(n—1)$$ so the recursive formula is $$f(0)=2$$ and $$f(n)=3\cdot f(n-1)$$

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