Question

An exponential function f ( x ) = a b x passes through the points (0, 4) and (2, 16). what are the values of a and b ?

Answer 1

a = 4 , b = 2

Explanation:

given the exponential function in the form

y = f(x) = a
`b^(x)`

use the given points f(x) passes through to find a and b

using (0, 4 ) , then

4 = a
`b^(0)` [
`b^(0)` = 1 ]

4 = a × 1 , so

a = 4

y = 4
`b^(x)`

using (2, 16 )

16 = 4 b² ( divide both sides by 4 )

4 = b² ( take square root of both sides )

`√(4)` = b , so

b = 2

then a = 4 and b = 2