Question

Write an exponential function for each set of points.

(0 , 1024), (1,256), (2,64). (3 , 16) and (4 ,4)

Answer 1

`f(x)=((1)/(4))^(x-b)`

Explanation:

We are given that

(0,1024),(1,256),(2,64),(3,16)and(4,4)

From given data we assume an exponential function

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

where b and a are constant

`f(0)=1024`

`1024=a^b`...(1)

`f(1)=256`

`256=a^(b+1)`...(2)

Equation (1) divided by equation (2)

Then, we get

`(1024)/(256)=(a^(b))/(a^(b+1))`

`4=a^(-1)`

`a=(1)/(4)`

Using the the value of a in equation (1)

`1024=((1)/(4))^(b)`

`4^(5)=4^(-b)`

`-b=5`

`b=-5`

Therefore, the exponential function

`f(x)=((1)/(4))^(x-b)`