Answer:
[tex]y =11(6)^x[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (0,11)[/tex]
[tex](x_2,y_2) = (2,396)[/tex]
Required
The exponential function
This is represented as:
[tex]y = ab^x[/tex]
In [tex](x_1,y_1) = (0,11)[/tex], we have:
[tex]11 = ab^0[/tex]
[tex]11 = a*1[/tex]
[tex]a = 11[/tex]
So, we have:
[tex]y = ab^x[/tex]
[tex]y = 11b^x[/tex]
In [tex](x_2,y_2) = (2,396)[/tex], we have:
[tex]396 = 11 * b^2[/tex]
Divide both sides by 11
[tex]36 = b^2[/tex]
Taks square roots
[tex]6 = b\\\\b=6[/tex]
So, we have:
[tex]y = 11b^x[/tex]
[tex]y =11(6)^x[/tex]
