Question

Suppose a set of data about the spread (in hundreds of acres) of a food-borne bacteria (after t weeks) in lettuce has the following percentage rates of change: 0.9%, 1.3%, 1.1%, 1.0%, 1.3%, 1.0%; and the following average rates of change: 2.9, 2.4, 3.7, 3.1, 3.6, 3.2. Based only on the information given, and without doing any calculations, what type of model would you use? Why? (NOTE THAT the information given is not the actual data set. I have calculated the two types of rate of change for you. You should NOT BE CALCULATING ANYTHING!) Comment:What tells you that the relation is best fit by a linear model? Use principles about what kinds of functions have consistency in which types of rates of change?

Answer 1

A sinusoidal model would be used

The kind of function that have consistency in the periodic rate of change is the Average rate of changes

Explanation:

The type of model that would be used is sinusoidal model and this is because there is periodic change in the values given ( i.e the rate of changes given )

For percentage rate of changes :

starting from 0.9% there is an increase to 1.3% then a decrease to 1.1% and a further decrease to 1% before an increase to 1.3% and another decrease to 1%

For Average rate of changes:

starting from 2.9 there is a decrease to 2.4, then an increase to 3.7 and another decrease to 3.1 followed by an increase to 3.6 and a decrease back to 3.2

This relation ( sinusoidal model ) is best suited for a linear model because there is a periodic rate of change in the functions

The kind of function that have consistency in the period rate of change is the Average rate of changes