Given: The graph of an exponential function as shown in the image
To Determine: The equation of the given graph
Solution
The general equation of an exponential equation is
[tex]\begin{gathered} y=ab^x \\ a=vertical\text{ stretch} \\ b=common-ratio \end{gathered}[/tex]
Let us pick a point from the graph and the value of common ratio to solve for a
Please note that the common ratio is 2 because the processing power doubles every year
So
[tex]\begin{gathered} Point:(0,60),b=2 \\ y=ab^x \\ 60=a(2)^0 \\ 60=a(1) \\ 60=a \\ a=60 \end{gathered}[/tex]
Let us substitute a and b into the general equation would given us
[tex]y=60(2)^x[/tex]
Hence, the equation is
y = 60 (2)ˣ
