Exponential Functions

An exponential function can in general be written in the form $$y=a\cdot b^x,$$ where $b$ is the function's value when $x=0,$ year $2016.$ We know that $a=20000,$ which means that the amount Billy G invested was $\$20000.$

$b$ specifies the exponential function's growth factor. In our model, $a=1.02$ which means that the investment is expected to increase by $2\%$ per year.

According to the model, $y$ dollars is the size of Billy G's investment, $x$ years after $2016.$ Therefore,

$$y\approx 23000\text{then}x=7$$ that the amount in the fund is approximately $\$23000,$ $7$ years after $2016,$ which means year $2016+7=2023.$