Question

Enter an equation for the function that includes the points.Give your answer in a(b)x. In the event that a=1 , give your answer in form (b)x. (2,2/3) and 3,5/9 The equation is f(x)=

Answer 1

`f(x) = (24)/(25) * (5)/(6)^x`

Explanation:

Given

`(x_1,y_1) = (2,(2)/(3))`

`(x_2,y_2) = (3,(5)/(9))`

Required

Write the equation of the function
`f(x) = ab^x`

Express the function as:

`y = ab^x`

In:
`(x_1,y_1) = (2,(2)/(3))`

`y = ab^x`

`(2)/(3) = a * b^2` --- (1)

In
`(x_2,y_2) = (3,(5)/(9))`

`y = ab^x`

`(5)/(9) = a * b^3` --- (2)

Divide (2) by (1)

`(5)/(9)/(2)/(3) = (a*b^3)/(a*b^2)`

`(5)/(9)/(2)/(3) = b`

`(5)/(9)*(3)/(2) = b`

`(5)/(3)*(1)/(2) = b`

`(5)/(6) = b`

`b = (5)/(6)`

Substitute 5/6 for b in (1)

`(2)/(3) = a * b^2`

`(2)/(3) = a * (5)/(6)^2`

`(2)/(3) = a * (25)/(36)`

`a = (2)/(3) * (36)/(25)`

`a = (2)/(1) * (12)/(25)`

`a = (24)/(25)`

The function:
`f(x) = ab^x`

`f(x) = (24)/(25) * (5)/(6)^x`