Functions (Mathematics)


  1. A leprechaun places a magic penny under a girl’s pillow. The next night there are 2 magic pennies under her pillow. The following morning she finds four pennies. Apparently, while she sleeps each penny turns into two magic pennies. The total number of pennies seen under the pillow each day is the grand total; that is, the pennies from each of the previous days are not being stored away until more pennies magically appear. How many days would elapse before she has a total of more than$10 billion?
  2. The following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the given question. A snowplow has maximum speed of 40 miles per hour on a dry highway. Its maximum speed decreases by 0.9 miles per hour for every inch of snow on the highway. According to this model, at what snow depth will the snow plow be unable to move?

The equation used to model this situation is ____where s is the maximum speed of the snowplow in miles per hour and d is the snow depth in inches.

  1. Suppose your dog weighed 2 pounds at birth and weighed 14.1 pounds one year later. Based on these two data points, find a linear function that describes how weight varies with age. Use this function to predict your dog’s weight at 4 and 10 years of age. Comment on the validity of this model.

The equation used to model this situation is _ where w is the weight of the dog in pounds and t is time in years.

  1. See attachment (question 9.C.29, A only)
  2. See attachment (question 9.C.31)
  3. A toxic radioactive substance with a density of 4milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 35 years ago. If the half- life of the substance is 20 years, what was the density of the substance when it was deposited 35 years ago? Answer in mg/cm squared.
  4. Between 2005 and 2009, the average rate of inflation was about 4.6% per year. If a cart of groceries cost $170 in 2005, what did it cost in 2009?