Write an exponential model for the data pairs (3,8), (5,2)

Answer 1

The general form of an exponential is y = ab^x

Plugging in the data points we get two equations:

1) 8 = ab³

2) 2 = ab⁵

Using Eq 1: a = 8/b³ and plugging that into Eq2 we get:

2 = (8/b³)b⁵

2/8 = b²

1/4 = b²

1/2 = b

Plugging that back into a = 8/b³ we get:

a = 8/(1/2)³

a = 8/(1/8)

a = 64

y = 64(1/2)^x