Answer:
Option D is correct
The exponential function is: [tex]f(x)= 4(3)^x[/tex]
Explanation:
An exponential function is in the general form is:
[tex]f(x) =ab^x[/tex]. ......[1]
Given the points (1,12) and (2, 36).
For the point (1,12),
Plug in x = 1 and y =12 in [1]; we get
[tex]12=ab^1[/tex] or
12 =ab ......[2]
Now, for the point (2, 36);
Plug in x= 2 and y =36 in [1];
[tex]36=ab^2[/tex] ......[3]
Divide equation [3] by equation [2], we have
[tex]\frac{36}{12}= \frac{ab^2}{ab}[/tex]
Simplify:
[tex]3= b[/tex]
Substitute the value of b in equation [2], to solve for a;
[tex]12 =a\cdot 3[/tex]
Divide both side by 3 we get;
[tex]\frac{12}{3}= \frac{3a}{3}[/tex]
simplify:
[tex]4 =a[/tex]
Then, put these a and b values in [1]; we get
The exponential function as: [tex]f(x)= 4(3)^x[/tex]
