Not all roles available for this page.
Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Noah is depositing money in his account every week to save money. The graph shows the amount he has saved as a function of time since he opened his account.
Elena opened an account the same day as Noah. The amount of money in her account is given by the function , where is the number of weeks since the account was opened.
Who started out with more money in their account? Explain how you know.
Who is saving money at a faster rate? Explain how you know.
There are four tanks of water.
The graph of the function for the amount of water in gallons, , in Tank D at time is shown. Is it filling up or draining out? How do you know?
On the first day after the new moon, 2% of the moon’s surface that we can see is illuminated. On the second day, 6% is illuminated.
Use this information to predict the days on which the moon’s surface that we can see is 50% illuminated and 100% illuminated.
When the sun was directly overhead, the stick had no shadow. After 20 minutes, the shadow was 10.5 centimeters long. After 60 minutes, it was 26 centimeters long.
Suppose a car is traveling at 30 miles per hour. The relationship between the time in hours and the distance in miles is a proportional relationship.
We can represent this relationship with an equation of the form , where distance is a function of time (since each input of time has exactly one output of distance).
Or we could write the equation instead, where time is a function of distance (since each input of distance has exactly one output of time).
These equations are examples of a mathematical model. A mathematical model is a mathematical object, like an equation, a function, or a geometric figure, that we use to represent a real-life situation. Sometimes a situation can be modeled by a linear function. We have to analyze the information we are given and use judgment about whether using a linear model is a reasonable thing to do. We must also be aware that the model may make imprecise predictions or may only be appropriate for certain ranges of values.
More generally, if we represent a linear function with an equation like , then is the initial value (which is 0 for proportional relationships), and is the rate of change of the function.
If is positive, the function is increasing.
If is negative, the function is decreasing.
If we represent a linear function in a different way, say with a graph, we can use what we know about graphs of lines to find the and values and, if needed, write an equation.