Period 4B - Math 1A: Unit 2 Review

1. You work 20 miles away from home.  When work is over, you head in the opposite direction of your home to meet a friend.  After driving for five minutes, you are 30 miles from home.  After 12 minutes, you are 44 miles from home.  After 40 minutes, you are 100 miles from home.
a. Is your distance from home as a function of time linear, exponential, or neither? How do you know?

• Exponential, because it has a multiplicative rate of change.
• Exponential, because it has an additive rate of change
• Linear, because it has an additive rate of change
• Linear, because it has a multiplicative rate of change

1. You work 20 miles away from home.  When work is over, you head in the opposite direction of your home to meet a friend.  After driving for five minutes, you are 30 miles from home.  After 12 minutes, you are 44 miles from home.  After 40 minutes, you are 100 miles from home.
b. Write a function rule that models this situation.  What are the independent and dependent variables, and what do they represent in this context?

• f(x)=20(2)^x
• f(x)=20(1.5)^x
• f(x)=-2x-20
• f(x)=2x+20

1.  You work 20 miles away from home.  When work is over, you head in the opposite direction of your home to meet a friend.  After driving for five minutes, you are 30 miles from home.  After 12 minutes, you are 44 miles from home.  After 40 minutes, you are 100 miles from home.

b.  What are the independent and dependent variables, and what do they represent in this context?
Independent Variable:
Dependent Variable:

• Independent: time
  Dependent: distance
• Independent: distance
  Dependent: time
• Independent: miles from home
  Dependent: time

In the function rule
f(x)=mx+b
What do m and b represent?

• m is the slope, b is the multiplicative rate of change
• m is the multiplicative rate of change, b is the y-intercept
• m is the additive rate of change, b is the initial value
• m is the initial value, b is the slope

2. You ingest 500mg of some medication.  After 1 hour, there is 420 mg left in your system.  After three hours, there is  296.352 mg left in your system.
a. Is the amount of medication left in your system as a function of time linear, exponential, or neither?  How do you know?

• Exponential, because it has a multiplicative rate of change.
• Exponential, because it has an additive rate of change
• Linear, because it has an additive rate of change
• Linear, because it has a multiplicative rate of change

2. You ingest 500mg of some medication.  After 1 hour, there is 420 mg left in your system.  After three hours, there is  296.352 mg left in your system.
b. Write a function rule that models this situation

• f(x)= -80x+500
• f(x) = (-2/5)x+500
• f(x)=500(1.19)^x
• f(x)=500(0.84)^x

In the function rule
f(x)=a(b)^x
What do a and b represent?

• a is the slope, b is the multiplicative rate of change
• a is the multiplicative rate of change, b is the y-intercept
• a is the y-intercept, b is the additive rate of change
• a is the initial value, b is the multiplicative rate of change

3. Ms. Roeck loves candles because they evoke a sense of peace and harmony. She keeps track of the lengths of her candles as she burns them.
b. Write a function rule that models this situation.

• f(x)= -0.1x-10
• f(x)= -0.1x+10
• f(x)= -1x+10
• f(x) = 1x+10

What is TRUE about the following function?

• The domain is from (0,infinity)
• The x-intercept is at (0,3)
• The y-intercept is (6,0)
• The slope or additive rate of change is 1/2

What is TRUE about the following function?

• The function is decreasing from (-infinity,infinity)
• As x-> infinity, y -> infinity
• The graph has a maximum at (6,0)
• The slope is 2/3