Question

(4.07) which of the following exponential functions goes through the points (1,12) and (2,36)

A. f(x) = 4(3)-x

B. f(x) = 3(4)-x

C. f(x) = 3(4)x

D. f(x) = 4(3)x​

Answer 1

D

Explanation:

The equation of an exponential function is

y = a
`(b)^(x)`

To find a and b, substitute (1, 12) and (2, 36) into the equation

(1, 12) → 12 = ab → (1)

(2, 36) → 36 = ab² → (2)

divide (2) by (1)

`(ab^2)/(ab)` =
`(36)/(12)`

b = 3

substitute b = 3 into (1)

12 = 3a ⇒ a = 4

f(x) = 4
`(3)^(x)` → D