MTH 134 – SU20
Lesson 29: Putting It All Together
For this problem-solving assessment, there is no piece that requires Excel. For these problems, please provide all of the work that you did to arrive at your answer. You may refer to your class notes and textbook and you may collaborate (not copy) with CLASSMATES. Any other assistance would be considered a violation of academic integrity. Make this submission of a quality that says you are a college student getting close to the point of being a professional! See the end of this document for the conversion factors you MUST use in this assessment as well as prefixes for SI units.
The solutions to this assessment will be posted in Blackboard (next to the link where you accessed this) shortly after the due date. That will allow students to use this as study material for the Final Exam.
- An important idea that I may not have stressed in the lesson – there is a difference between a growth RATE and a growth FACTOR for an exponential function! Let F stand for the growth FACTOR and R stand for the growth RATE as a decimal (as compared to a percentage.) SO, in a nutshell: F = 1 + R . Now, that rate COULD be negative in the case of exponential decay – such as the value of your new car as you leave the dealership or as in radioactive decay. Using my variables, the exponential function would be written as: , where C stands for the initial value (condition). (For more info, read section 7.5 in your text.)
EX: For , the initial value is 250 and is growing with a growth factor of 1.45, a 45% growth RATE. NOTE: 145% – 100% = 45%.
EX: For , the initial value is 84 and is decaying with a growth factor of 0.74, a decay RATE of 0.26 or 26%, or a growth RATE of -26%. NOTE: 100% – 74% = 26%.
Try the following for yourself. Fill in the missing information. Use C for initial value. (3 pts ea row)
| Function | Growth Factor | Growth Rate (as %) |
| 33.07% | ||
| 1.019 | ||
- The Yangtze River in China is 6380 km long. The length of the beautiful floating river in Arkansas, the Buffalo River, is 153 miles long.
- How much longer is the Yangtze than the Buffalo? Include units. More than one answer is possible. (7 pts)
- Compare the lengths of the two rivers using orders of magnitude. Write a complete sentence to describe the relationship. (4 pts)
- According to our text, the United Kingdom generated approximately 53 terawatt-hours of nuclear energy in 2008, when its population was about 60 million. In the same year, the US generated 805 terawatt-hours for a population of about 309 million. Give answers in scientific notation and, if necessary, round the coefficient to the nearest 0.001. (12 pts)
- How many kilowatt-hours (kwH) did the UK generate per person in 2008? Note: The basic unit of power is watt-hour and then the prefixes are applied to that base unit.
- How many kilowatt-hours (kwH) did the US generate per person in 2008? Note: The basic unit of power is watt-hour and then the prefixes are applied to that base unit.
- Write a brief statement comparing the relative magnitude of the generating of nuclear power between the two countries in 2008.
- Two people are found to have lung cancer tumors with volumes of 0.5 cubic centimeters. The former asbestos worker’s tumor (A) is expected to double every 8 months. A heavy smoker’s tumor (S) is expected to double every 2 months. Give values to the nearest 0.001 (18 pts)
- Write a function for the growth of the tumor of the heavy smoker where S is the volume of the tumor and t is the number of 2-month time periods.
- Based on your model from part a, what is the expected volume of the tumor after 24 months?
- Write a function for the growth of the tumor of the asbestos worker where A is the volume of the tumor and t is the number of 2-month time periods. Note – since this person’s tumor doubles every 8 months, think about how you can adjust (with multiplication or division) to set up the equation so that after 8 months (4 doubling periods), the volume has doubled ONCE.
- Based on your model from part c, what is the expected volume of the tumor after 24 months?
- Assuming both tumors grow in a spherical shape, find the DIAMETER of each, in cm, after 24 months. The formula for the volume of a sphere:
Asbestos Worker:
Heavy Smoker:
- Determine which of the following functions are linear, exponential or neither? Give the initial condition and the ARC or Growth Factor for the linear or exponential model in the table below. Work should be shown as calculations. No explanations needed. Hint: Check ARC and then consider possible exponential function and see if it holds. (16 pts)
| Function | Linear, Exponential Or Neither? |
Initial Condition |
ARC or Growth Factor |
| f | |||
| g | |||
| h | |||
| j |
- Make a table of values (rounded to two non-zero digits – like 43,508.79 goes to 44,000) and plot the following function on the semi-log plot. Be sure to indicate your scale on the vertical axis. (16 pts)
| x | y |
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 |
|
|
|
- The graph to the right shows the amount of a drug dose D, in mg, that is still in a patient’s body t hours after the dose was given. (12 pts)
- Estimate the initial dosage, including units.
- Estimate the half-life of the drug, in hours.
- Use your estimates to write an equation that can be used to approximate the amount of this drug that remains in a patient’s body. Use the variables given above.
- Use your equation to estimate the amount of the drug still in the patient’s body after five half-lives. Use an arrow on the graph above to show where that value is located. Mark that location with an A.
A Few Conversion Factors
1 mile ≈ 1.609 km
1 foot ≈ 30.48 cm
5280 ft = 1 mile
I kg ≈ 2.2 pounds
100 cm = 1 m
