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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
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,
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
Or we could write the equation
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
If
If
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.
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