Determine whether the table could represent a function that

Determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find the exponential function that passes through the points. (If an answer does not exist, enter DNE.)

Solution

x        1      2       3         4

h(x)    80   64     51.2    40.96

ratio       .8      .8       .8

Here the ratio is constant so its exponential.

And exponential equation is of the form

y=ab^x

We have points (1,80) , (2,64)

From these two points we get

80= a b¹        and       64= a b²

From these two equations we get

b= .8     and   a= 100

Therefore required equation is

y= 100*.8^x