Question #cba2e

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Bill K.
Oct 11, 2015

D. #log(f)# vs. #x#

Explanation:

If #f# is exponential, then #f(x)=a * b^(x)# for some constants #a>0# and #b > 0#. Taking the log of both sides results in #log(f(x)) = log(a * b^{x})#. By properties of logarithms, this becomes #log(f(x))=log(a) + x * log(b)#. This shows that #log(f)# is a linear function of #x#.

This can be thought of in terms of data as well. For example, the data points #(2,3.312)#, #(3,3.9744)#, and #(4,4.76928)# are approximately exponential because #(2,log(3.312)) approx (2,0.52)#, #(3,log(3.9744))approx (3,0.60)#, and #(4,log(4.76928))approx (4,0.68)# are approximately linear.

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