Answered

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Which of the function correctly expresses the exponential model f(x)=6(14)^x with base of e

Sagot :

facundo3141592

The exponential equation with a base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

How to change the base?

We start with:

[tex]f(x) = 6*(14)^x[/tex]

We want to rewrite this to:

[tex]f(x) = 6*(e^n)^x[/tex]

So we only need to find the value of n such that:

[tex]e^n = 14[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]

Then the exponential equation with base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

If you want to learn more about exponentials:

https://brainly.com/question/11464095

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