Question

Which of the following exponential regression equations best fits the data shown below? A. y = 3.02 × 3.67^x B. y = 2.27 × 2.097^x C. y = 6.61 × 1.55^x D. y= 8,04 × 0.98^x

Answer 1

For solving this problem we must use a calculator or software that allows us to do an exponential regression.

Using a calculator, for example, we introduce the values of x and y and then we adjust an exponential function of the form:

`y=A\cdot e^(k\cdot x)`

Where A and k are the parameters to adjust. So solving with a calculator or software we get to this table of data the following result:

`\begin{gathered} A\cong6.6114 \\ k\cong0.4378321 \end{gathered}`

Now, taking into account that we can rewrite the function above in the following form:

`\begin{gathered} y=A\cdot B^x \\ B=e^k\cong1.549344 \end{gathered}`

We see that the adjustment is approximately:

`y=6.61\cdot1.55^x`

So the correct answer is: C. y = 6.61 × 1.55^x