Question

Which of these exponential functions goes through the points (1, 12) and (2, 36)?

Answer 1

Answer:

Option D is correct

The exponential function is: $f(x)= 4(3)^x$

Explanation:

An exponential function is in the general form is:

$f(x) =ab^x$.                ......[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

$12=ab^1$ or

12 =ab                  ......[2]

Now, for the point (2, 36);

Plug in x= 2 and y =36 in [1];

$36=ab^2$                   ......[3]

Divide equation [3] by equation [2], we have

$\frac{36}{12}= \frac{ab^2}{ab}$

Simplify:

$3= b$

Substitute the value of b in equation [2], to solve for a;

$12 =a\cdot 3$

Divide both side by 3 we get;

$\frac{12}{3}= \frac{3a}{3}$

simplify:

$4 =a$

Then, put these a and b values in [1]; we get

The exponential function as: $f(x)= 4(3)^x$