## How Is The Slope Of A Function Interpreted?

The slope is best understood by looking at the units of the independent and dependent variable. The units are always the units on the dependent variable per the units on the independent variable. This problem illustrates this fact.

Problem 1 The percent p of high school seniors who ever used marijuana can be related to x, the number of year after 2000, by the equation 25p + 21x = 1215.

a. Use this model to determine the slope of the graph of this function if x is the independent variable.

b. What is the rate of change of the percent of high school seniors using marijuana per year?  This last part indicates that each year, the percentage drops by 0.84 percent.

## How Are Inputs and Outputs Related Through A Model?

When working with a model, you need to pay careful attention to the units on each variable.

Problems 1 The number y (in millions) of women in the workforce is given by the function \$latex \displaystyle y=0.006{{x}^{2}}-0.018x+5.607\$ where x is the number of years after 1900.

a. Find the value of y when x = 44. Explain what this means.

b. Use the model to find the number of women in the workforce in 2010. This week you will be graphing the function from Project 3. To find the equation for this function, you need to utilize the initial population and doubling time of the population. The goal of this post is to help you to find the rate r in the function \$latex displaystyle A(t)=P{{e}^{rt}}\$. You will need to use the doubling time assigned to you in the project letter to do this.