Question

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

Exponential models
Find a recursive rule that models the exponential growth of $$\displaystyle{y}={2}{\left({1.08}\right)}^{{t}}$$
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 $$\displaystyle{f{{\left({t}+{1}\right)}}}={1.08}\cdot{f{{\left({t}\right)}}}$$