Question

Write an exponential function in the form y = ab that goes through points (0,4)
and (2, 196).

Answer 1

y = 4
`(7)^(x)`

Explanation:

The form of the exponential function is y = a
`b^(x)`

Use the given points to solve for a and b

Using (0, 4 ), then

4 = a
`b^(0)` (
`b^(0)` = 1 ), thus a = 4

y = 4
`b^(x)`

Using (2, 196 ), then

196 = 4b² ( divide both sides by 4 )

49 = b² ( take the square root of both sides )

b =
`√(49)` = 7

y = 4
`(7)^(x)` ← exponential function