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Write an exponential function for each set of points.

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

1 Answer

8 votes

Answer:


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)

User Abdul Razak Zakieh
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