SOLUTION: The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. HINT [See Example 1.]

Question 1164874: The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. HINT [See Example 1.] (If an answer does not exist, enter DNE.)
x −2 −1 0 1 2
f(x) 1.125 2.25 4.5 9 18
g(x) 12
6 3 1.5 0.75
f(x) =

g(x) =

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The first is exponential with f(x)=4.5*2^x
look at when x=0. Then a must be 4.5
9 is 4.5 *2 and 18 is 4.5*4 and (1/2) and (1/4) for the negative values of x
for the second, ab^x=3 when x=0 so a=3
when x=1 3b^1=1.5 so b=(1/2)
when x=-1 3b^1=3*2 or 6, flipping the fraction with a negative exponent (1/2)^-1 is 2
it is exponential and 3*0.5^x=f(x)
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