1 Answer

Jennie · Answer 1 · 2023-07-21T20:25:46+0000

As you have already written, the exponential function have the following form:

$\begin{gathered} y=B(C)^x \\ B,C\in\mathfrak{\Re } \end{gathered}$

With the given points

$\lbrace(0,12),(1,3)\rbrace$

We can make a substitution in the general form and find the coefficients "B" and "C".

Making the substitution:

$y(0)=12\Rightarrow B(C)^0=12\Rightarrow B=12$
$y(1)=3\Rightarrow12(C)^1=3\Rightarrow C=(3)/(12)=(1)/(4)=0.25$

With this, we have the values for our coefficients, and we can make the substitution in the general form:

$\begin{gathered} y=B(C)^x \\ \begin{cases}B=12 \\ C=0.25\end{cases}\Rightarrow y=12(0.25)^x \end{gathered}$

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