Question

Find the exponential function f(x)=Ca^x whose graph is given below.

Answer 1

f(x) = 2
`((1)/(3)) ^(x)`

Explanation:

exponential in the form

f(x) = C
`a^(x)`

to find C and a use points from the graph

using (0, 2 ) , then

2 = C
`a^(0)` (
`a^(0)` = 1 ) , so

C = 2

f(x) = 2
`a^(x)`

using (2,
`(2)/(9)` )

`(2)/(9)` = 2a² ( divide both sides by 2 )

`(1)/(9)` = a² ( take square root of both sides )

`\sqrt{(1)/(9) }` = a ⇒ a =
`(1)/(3)`

f(x) = 2
`((1)/(3)) ^(x)` ← exponential function