How do you Find the exponential growth function for a given data set?

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Answer 1 · 2014-11-07T17:07:14

Example

Find the exponential function #f(x)=Ca^x# that passes through the points #(1,15)# and #(3,375)#.

#{((1,15) => f(1)=Ca=15),((3,375) => f(3)=Ca^3=375):}#

By dividing #f(3)# by #f(1)#,

#{f(3)}/{f(1)}={Ca^3}/{Ca}=a^2={375}/{15}=25 => a=pm 5#

Since the base of an exponential function cannot be negative, we have #a=5#.

By plugging into the first equation,

#C cdot 5=15 => C=3#

Hence, the exponential function is

#f(x)=3 cdot 5^x#

I hope that this was helpful.