Question

I need help on number 14 and not sure if I got the right answer and did the table right help please :( !!

Answer 1

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}`