Question

# Find a recursive rule that models the exponential growth of y=1800(1.11)^t

Exponential models
Find a recursive rule that models the exponential growth of $$\displaystyle{y}={1800}{\left({1.11}\right)}^{{t}}$$
The functional form the given equation can be written as $$\displaystyle{f{{\left({t}\right)}}}={1800}{\left({1.11}\right)}^{{t}}$$ where f(0)=1800 and 1.11 is the ratio of successive values of the function.
That is, $$\displaystyle\frac{{f{{\left({1}\right)}}}}{{f{{\left({0}\right)}}}}=\frac{{f{{\left({2}\right)}}}}{{f{{\left({1}\right)}}}}=\ldots=\frac{{{f{{\left({t}+{1}\right)}}}}}{{f{{\left({t}\right)}}}}=\ldots={1.11}$$
So the recursive rule for this function van be written as $$\displaystyle{f{{\left({t}+{1}\right)}}}={1.11}\cdot{f{{\left({t}\right)}}}$$