MAT 084 - Mr. JohnsName
Modeling – Applying Math to Real World Data
1. a) Plot the data (0,-2) and (6,6) on the axes to the right.
Connect them with a line.
b) Find the equation of this line (model).
y =
Check your model by using the second data point above.
c) Use your model to predict the x-value when y = −6.
Does it agree with the line you drew?
2. A farmer starts out with 10 rabbits. After 12 months,
he has 70 rabbits.
If x is the number of months since the start,
then y is the number of rabbits.
a) Write the information above as two data points.
( , )( , )
Now plot these data on the axes to the right. Be sure
to scale your axes appropriately. Include units on your axes.
Then connect the data with a straight line.
b) Find the model.
y =
c) Explain what the slope of the model tells you about the rabbits.
d) When will the farmer have 200 rabbits?
3. The air pressure at sea level in Seattle is 30 pounds
per square inch (psi). At SnoqualmiePass (elevation 4000 feet),
the air pressure drops to 25 psi.
If x is the elevation above sea level in feet,
then y is the air pressure in psi.
a) Plot the given information on the axes to the right.
Be sure to scale and label the units on the axes.
Then connect your data with a line.
b) Find the model for the air pressure.
y =
c) Explain what the slope of the model tells you about air pressure.
d) What is the air pressure on top of Mt.Rainier (elevation 14000 feet)?
e) At what elevation is there no air pressure according to this model?
4. A phone card charges a 25¢ connection fee for each call.
If you talk for 15 minutes, the total charge is 70¢ for the call.
If x is the number of minutes you talk for a call,
then y is the total charge for the call in cents.
a) Model the data above with a straight line
on the axes to the right.
b) Find the model for the cost of a call.
y =
c) Carefully explain what the slopeof the model
tells you about your call.
d) Looking at the data, if you talk for 15 minutes, it costs you 70¢ for15 minutes or 4⅔¢ per minute. Yet the phone card claims you pay only 3¢ a minute. Are they correct? Explain.
e) How many minutes do you get for a $5 phone card?