Answer Key – Increasing Portions, Expanding Waist Lines
1. Write a linear function that describes this woman’s weight, W, after t weeks if she consumes
c calories a day.
 7 c  2160 
W  165  
t

3500 
2. Take the 2160 calories our friend from part one needed to maintain her healthy weight and
calculate a 60% and 33% increase. How many calories does she eat a day after each of these
increases?
33% increase: 2873 calories/day
60% increase: 3456 calories/day
3. Use the function you wrote in Question 1 to write an equation that models her weight if her
daily calories increased 33% and 60% from what she needs to maintain the same weight.
Write the functions and draw a graph for each below.
 7 2872.8  2160 
 4989 
t  165  
t  165  1.43t
33% increase: W  165  

 3500 


3500
© 2011 National Council of Teachers of Mathematics
http://illuminations.nctm.org
 7 3456  2160 
 9072 
60% increase: W  165  
t  165  
t  165  2.59t

 3500 


3500
4. Use the function to predict how much she would weigh after 1 month, 6 months, 1 year, 5
years, and 10 years.
WEIGHT AFTER 60%
1 month (4.2 weeks)
WEIGHT AFTER 33%
INCREASE
170.0 lbs
6 months (25.2 weeks)
201.0 lbs
230.3 lbs
1 year (52 weeks)
239.4 lbs
299.7 lbs
5 years (260 weeks)
536.8 lbs
838.4 lbs
10 years (520 weeks)
908.6 lbs
1511.8 lbs
TIME
INCREASE
175.9 lbs
© 2011 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Students may convert weeks slightly differently (for example, 4 weeks = 1 month)
or they may convert to different units.
5. On the same axes, make a graph of her weight if she a) eats the amount of calories she needs
to maintain her weight b) eats 33% more than that and c) eats 60% more than that.
6. What impact are the increased portion sizes having on her weight over time?
The extra calories are making her weight steadily increase over time.
© 2011 National Council of Teachers of Mathematics
http://illuminations.nctm.org