Exponential Functions and Models

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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.)
f(x) = 
g(x) = 
Jul 9th, 2015

Thank you for the opportunity to help you with your question!

assume that f = a*b^x 

then we have f(1)/f(0) = b  = 1/2 

f(0) = a = 0.5 

f(x) = 0.5*(1/2)^x 

f(-2) = 0.5*(1/2)^(-2) = 0.5*4 = 2 but we have f(-2) = 4, so answer is DNE


assume g(x)=  a*b^x 

b = g(1)/g(0) = 1/2 

a = g(0) = 100 

g(x) = 100*(1/2 )^x

g(2) = 100*(1/2)^2 = 25 

but we have g(2) = 10, so answer is DNE

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 9th, 2015

This makes much more sense now that I can actually see that the answer DNE. Thanks for taking the time to help me out! 

Jul 9th, 2015

you are welcome

Jul 9th, 2015

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