Question

Find a recursive rule that models the exponential growth of y=2(1.08)^t

Exponential models
ANSWERED
asked 2021-06-14
Find a recursive rule that models the exponential growth of \(\displaystyle{y}={2}{\left({1.08}\right)}^{{t}}\)

Answers (1)

2021-06-15
The functional form the given equation can be written as \(\displaystyle{f{{\left({t}\right)}}}={2}{\left({1.08}\right)}^{{t}}\) where f(0)=2 and 1.08 is the ratio of succesive values of the function.
That is, \(\displaystyle\frac{{f{{\left({1}\right)}}}}{{f{{\left({0}\right)}}}}=\frac{{f{{\left({2}\right)}}}}{{f{{\left({1}\right)}}}}=\ldots=\frac{{{f{{\left({t}+{1}\right)}}}}}{{f{{\left({t}\right)}}}}=\ldots={1.08}\) So, the recursive rule for this function van be written as \(\displaystyle{f{{\left({t}+{1}\right)}}}={1.08}\cdot{f{{\left({t}\right)}}}\)
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