Quiz 5.2 Review 9/22 PDF

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Document about using the recursive and exponential function in word problems....

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Name:__________________________________ Date_______________ Period______ Quiz 5.2 Review 1. Steven decides to take a job at the Apple Store selling iPhones. He is paid a base salary of $1,200 a month and then earns $10.50 for each new iPhone he sells. a. Should this situation be represented with Linear Recursion or Exponential Recursion?

b. Write a recursive rule describing his monthly income for selling iPhones.

c. Write a function rule describing his monthly income for selling iPhones.

2. As our population uses more antibiotics for minor infections, bacteria adapt and become resistant to the medications that are available. Methicillin-resistant Staphylococcus aureus (MRSA) is strain of Staphylococcus bacteria that is resistant to antibiotics. MRSA causes skin and respiratory infections and can be fatal. The Center for Disease Control (CDC) reported that in the United States 94,360 MRSA infections occurred in 2005, with 18,650 of these cases resulting in deaths. To put this number in perspective, CDC reported 16,316 deaths in 2005 related to AIDS. A research lab is observing the growth of a new strain of MRSA in an agar dish. The initial area occupied by the bacteria is 2 square millimeters. In previous experiments with MRSA, scientists observed the bacteria to increase by 20% each week. a. Write a recursive rule for the area (a) of the bacteria after n weeks.

b. Fill in the table, showing the increase in area of the bacteria over 5 weeks. c. Then make a scatterplot of the data. Week 0 1 2 3 4 5

Process

Area 2 (mm ) 2

3. Write a function rule that models the area of MRSA bacteria in terms of the number of weeks they grow. Graph the function rule with your scatterplot to check the rule.

4. Use the function rule to predict the area of the MRSA bacteria after 25 weeks.

5. Below is a set of data showing the temperature (degrees Fahrenheit) of a cup of hot liquid, such as coffee, changing over time (minutes). Complete the table by computing the first differences and successive ratios. Use your calculator to help with the computation.

0

Temperature of Liquid (L) – Room Temperature (T) 90.6

1 2

88.2 85.8

3

83.6

4

81.5

5

79.6

6 7

77.8 76.1

8 9

74.4 73.2

10

72.0

Time ( t)

First Differences (ΔT)

Successive Ratios

6. Is the relationship between time and temperature linear or exponential? How do you know?

7. Use the information in the table to build a recursive rule for the difference in temperature from room temperature for each successive temperature reading.

8. Sketch a scatterplot, with accuracy and detail, of temperature versus time. Use your calculator to verify your sketch.

x

9. The general form for an exponential function is y = a(b) , where a represents the initial condition and b represents the successive ratio, or base of the exponential function. Using data from your table, write a function rule to describe the temperature of the coffee (y) as a function of time (x).

10.Graph the function rule over the data in your scatterplot. Sketch your results....