Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 3)(0,3) and (4, 7203)(4,7203).

Answer 1

`y = 3(7)^x`

Explanation:

Given

`(x_1,y_1) = (0,3)`

`(x_2,y_2) = (4,7203)`

Required

Determine an exponential function

Substitute 0 for x and 3 for y in
`y=ab^x`

`3 = ab^0`

`3 = a*1`

`3 = a`

`a = 3`

Substitute 4 for x and 7203 for y in
`y=ab^x`

`7203= ab^4`

Substitute 3 for a

`7203= 3*b^4`

Divide both sides by 3

`2401= b^4`

Take 4th root of both sides

`\sqrt[4]{2401} = b`

`7 = b`

`b = 7`

Substitute 3 for a and 7 for b in
`y=ab^x`

`y = 3(7)^x`