Question

Write an exponential function in the form y = abx that goes through points (0,16)
and (2,400).​

Answer 1

y = 16
`(5)^(x)`

Explanation:

Use the given points to find the values of a and b

Using (0, 16), then

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

a = 16

y = 16
`b^(x)`

Using (2, 400), then

400 = 16b² ( divide both sides by 16 )

b² = 25 ( take the square root of both sides )

b =
`√(25)` = 5

Thus

y = 16 ×
`5^(x)` ← exponential function