The graphs below are exponential function graphs, the general formular takes the form
[tex]y=ab^x[/tex]
The graph of
[tex]y=50(1.5)^x[/tex]
Is shown below
The graph of
[tex]y=50(2^x)[/tex]
Is shown below
The graph of
[tex]y=50(2.5^x)[/tex]
Is shown below
Hence,
[tex]\begin{gathered} y=50(1.5)^x\rightarrow C \\ y=50(2)^x\rightarrow B \\ y=50(2.5)^x\rightarrow A \end{gathered}[/tex]
The equation of the exponential function is
[tex]\begin{gathered} y=ab^x \\ a=50\rightarrow the\text{ initial value} \\ b\rightarrow growht\text{ factor} \end{gathered}[/tex]
Thus the higher the growth factor the greater the rate of attaining a higher value within a short period.
That is why you see that the function with growth factor of 2.5 grows faster than that of 2 and also 1.5.
So the at x value of 3, the function with the greatest growth factor will have the highest y-value.
This implies , growth factor of 2.5 will have the highest, that corresponds to graph with colour green. Function with growth factor 2 will be the next to that of 2.5, that is red colored graph, and the last will be blue.
