the Explanation
The model in the table represents an exponential model with the general equation below.
[tex]y=ab^x[/tex]
We can then get the actual model by substituting two given values from the table.
When x= 0 and y = -5
[tex]\begin{gathered} -5=ab^0 \\ a=-5----1 \end{gathered}[/tex]
When 1 = 0 and y= -15
[tex]\begin{gathered} -15=ab^1 \\ \therefore ab=-15----2 \end{gathered}[/tex]
We can then substitute a = -5 in equation 2.
[tex]\begin{gathered} -5b=-15 \\ b=\frac{-15}{-5} \\ b=3 \end{gathered}[/tex]
Therefore
The model can be written as;
[tex]y=-5(3)^x[/tex]
