Question

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 \(f(n) = b\cdot f(nā€”1)\) so the recursive formula is \(f(0)=2\) and \(f(n)=3\cdot f(n-1)\)

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