Question

(Exponential Regressions)The accompanying table shows the number of bacteria present in a certain cultureover a 4 hour period, where x is the time, in hours, and y is the number ofbacteria. Write an exponential regression equation for this set of data, rounding allcoefficients to the nearest hundredth. Using this equation, determine the number ofbacteria present after 16 hours, to the nearest whole number.

Answer 1

`\begin{gathered} (a)y=460.30(1.10)^x \\ (b)2115\text{ bacteria} \end{gathered}`

Step-by-step explanation:

Part A

An exponential regression is of the form:

`y=AB^x`

We plug this data into an exponential regression calculator:

To the nearest hundredth, the values obtained are:

`\begin{gathered} A\approx460.30 \\ B\approx1.10 \end{gathered}`

An exponential regression equation for this set of data is:

`y=460.30(1.10)^x`

Part B

After 16 hours, when x=16

`\begin{gathered} y=460.30(1.10)^(16) \\ y\approx2115\text{ (to the nearest whole number)} \end{gathered}`

After 16 hours, the number of bacteria present is 2,115.