Question

Write an exponential function y = ab^x for a graph that includes (2, 24) and (3, 48).

A. y = 6(2)^x
B. y = 3(4)^x
C. y = 4(3)^x
D. y = 2(6)^x​

Answer 1

A

Explanation:

Substitute the x and y values from the given points into the equation and solve for a and b

Using (2, 24), then

24 = ab² → (1)

Using (3, 48), then

48 = ab³ → (2)

Dividing (2) by (1)

`(ab^3)/(ab^2)`=
`(48)/(24)`, hence b = 2

Substitute b = 2 into (1)

24 = a × 2² = 4a ( divide both sides by 4 )

a = 6

Hence equation is y = 6
`(2)^(x)` → A