Question

27-28 For each scatter plot, decide what type of function you might choose as a model for the data. Explain your choices.

Short answer

a. \(y = a \cdot {b^x} + c\)

b. \(y = \frac{a}{x}\)

Step-by-step solution

Find the model for graph (a) 

The data points in graph (a) are increasing exponentially, and they are at a certain distance from the origin.

\(y = a \cdot {b^x} + c\)

Find the model for graph (b) 

The values of data points in graph (b) are decreasing towards the right. So, the appropriate model is

\(y = \frac{a}{x}\).

Find the change in energy E with an increase in temperature

From the graph of \(E\left( T \right)\), with an increase in temperature, the energy initially increase slowly, and after a while, it increases at a higher rate.