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.