Question

Write a possible exponential function in y=ab^x form for the graph described below.

-> Passes through the points (0,2) and (3,0.25).

Answer 1

see explanation

Explanation:

Substitute the given points into the equation and solve for a and b

Using (0, 2 ), then

2 = a.
`b^(0)` →
`b^(0)` = 1, thus

a = 2

The equation is

y = 2
`b^(x)`

Using (3, 0.25 ), then

0.25 = 2. b³ ( divide both sides by 2)

b³ = 0.125 ( take the cube root of both sides )

b = 0.5

Hence a possible exponential function is

y = 2
`(0.5)^(x)`