Let's begin by identifying key information given to us:
[tex](t,b)=(0,500),(1,475),(2,451.25),(3,428.69),(4,407.25),(5,386.89)[/tex]
We will proceed to calculate for the slope of this function. We have:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{475-500}{1-0}=\frac{451.25-475}{2-1}\Rightarrow\frac{-25}{1}=\frac{-23.75}{1} \\ m=-25\ne-23.75 \\ \therefore This\text{ is not a linear function} \\ \end{gathered}[/tex]
We will proceed to find the common ratios as shown below:
[tex]\begin{gathered} r=\frac{475}{500}=\frac{451.25}{475}\Rightarrow\frac{95}{100}=\frac{95}{100}=0.95 \\ r=\text{0}.95 \\ \therefore\text{This is an exponential function} \\ \\ \end{gathered}[/tex]
This exponential equation is given by:
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