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Find either an exponential or linear function that models the data in the table.

Find either an exponential or linear function that models the data in the table.
 
 
x   -3             - 2          -1             0           1
________________________________________
y  16,384      4096       1024        256        64
 
 
F(x) = ?
 
(use intergers or fractions for any numbers in the expression)

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2 Answers

y = a b^x

256 = a b^0

a = 256

y = 256 b^x

64 = 256 b^1

b = 64/256 = 1/4

y = 256(1/4)^x

y = (2^8)(2^(-2x))

y = 2^(8-2x)

check:

2^(8-2(-1)) = 2^10 = 1024

2^(8-2(-2)) = 2^12 = 4096

2^(8-2(-3)) = 2^14 = 16384