Question

An exponential function f ( x ) = a b x passes through the points (0, 2000) and (2, 720). what are the values of a and b ?

Answer 1

a = 2000 , b = 0.6

Explanation:

given the equation of the exponential has the form

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

use the coordinates of the points f(x) passes through

using (0, 2000 ) , then

2000 = a
`b^(0)` [
`b^(0)` = 1 ]

2000 = a × 1 = a , then

y = 2000
`b^(x)`

using (2, 720 )

720 = 2000 b² ( divide both sides by 2000 )

0.36 = b² ( take square root of both sides )

`√(0.36)` = b

b = 0.6

so a = 2000 and b = 0.6