Math 100: Test Three Solutions - Population and Decay Rates, Exams of Quantitative Techniques

Download Math 100: Test Three Solutions - Population and Decay Rates and more Exams Quantitative Techniques in PDF only on Docsity!

Math 100 Spring 2007

Test Three Solutions

Directions: Show all work in the space provided.

Unsupported answers may not receive credit.

Name:

1. The population of Tukeytown is increasing at a rate of 13% per year. a) (2 pts) Is this linear growth, linear decay, exponential growth, or exponential decay? b) ( 6 pts) If the population is 12,000 today, what will it be in 10 years? Round your answer to the nearest person. 10 12,000 (1.13) 40,
2. The population of Trigsburg is decreasing at a rate of 500 people per year. a) (2 pts)Is this linear growth, linear decay, exponential growth, or exponential decay? b) (6 pts)If the population is 20,000 today, what will it be in 4 years? Round your answer to the nearest person. 20,000  4 500 18,
3. The value of your car is decreasing by 6% each year. a) (2 pts) Is this linear growth, linear decay, exponential growth, or exponential decay? b) (6 pts)If you bought the car for $15,000, what will it be worth in 5 years? Round your answer to the nearest penny. 5 15,000 (1  .94) 11008.
4. The cost to rent a car is a flat fee of $80 plus $.25 for each mile driven. a) (4 pts) Write an equation to represent the cost C , as a function of mileage, m. C $80 $.25 m b) (4 pts) Determine the cost to the nearest penny to rent the car if you wish to travel a total of 350 miles. C  $80  $.25(350) $167.
   c) (4 pts) How far can you travel for $400?

7. The table below indicates how the concentration of a chemical in a public pool changes with the number of days that pass after regular maintenance of the pool. In other words, the concentration is a function of time (in days). Days after regular maintenance Concentration in parts per million (ppm) 2 7. 8 6 12 5 a) (2 pts) Which of these variables is the independent (input) variable? Days (time) b) (2 pts) Which of these variables is the dependent (output) variable? concentration c) (6 pts) Use the axes below to make a graph of this function. Be sure to clearly label and title both axes.

8. The graph below represents the concentration (in parts per million) of a drug in a patient’s bloodstream each day after the start of medical treatment. 0 1 2 3 4 5 6 7 0 5 10 15 Days Concentration (ppm) a) (2 pts) Use the graph of the function to find the concentration on day 5. 4 ppm b) (2 pts)Use the graph to find the day on which the concentration is 4.5 ppm. day 7 c) (2 pts)What is the initial drug concentration? 3 ppm d) (4 pts) Find the rate of change of the drug over time. Be sure to include units in your answer. 6 3 3 1 / 15 0 15 5 slope ppm day

e) (2 pts) What is the independent variable in this situation? days (2 pts) What is the dependent variable? concentration f) (4 pts) Use your answers to (c-f) to write a linear equation that expresses the drug concentration as a function of the number of days after the start of medical treatment. 1 concentration   3 5 ( days )

9. The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours. Suppose that a patient receives an initial dose of 10 mg of Valium at 6 pm. a) (4 pts) Write an exponential equation to represent the amount of Valium in the bloodstream at time t. 10 (.5) 36 t V   b) (4 pts) How much Valium is in the patient’s blood at midnight? (^636) V  10 (.5)  8.91 mg c) (4 pts) When will there be 5 mg of Valium left in the patient’s blood?