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Practice

5.8.5 Practice

5.8.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. For an experiment, a scientist designs a can, 20 cm in height, that holds water. A tube is installed at the bottom of the can allowing water to drain out. At the beginning of the experiment, the can is full. Every minute after the start of the experiment, 2 3 of the water is drained.

    The height of the water, h , in cm, is a function f of time t  in minutes since the beginning of the experiment, h = f ( t ) . Which is an expression for f ( t ) ?
  1. f ( t ) = 20 + 2 3 t
  2. f ( t ) = 20 ( 2 3 ) t
  3. f ( t ) = 20 ( 1 3 ) t
  4. f ( t ) = 20 + 1 3 t
  1. A bacteria population is 10,000. It triples each day.
    The bacteria population, b , is a function of the number of days, d . Which equation relates b and d ?
  1. b = 10000 + 3 d
  2. b = 10000 ( 1 3 ) d
  3. b = 10000 ⋅ 3 d
  4. b = 10000 ⋅ 3 d
  1. The area, a , covered by a city is 20 square miles. The area grows by a factor of 1.1 each year, t , since it was 20 square miles. Which equation expresses a in terms of t ?
  1. a = 20 − 1.1 t
  2. a = 20 ⋅ 1.1 t
  3. a = 20 ⋅ 1.1 t
  4. a = 20 + 1.1 t
  1. The graph below models the water draining out of a tube during an experiment represented by the function, f ( t ) = 20 ( 1 3 ) t . What does the value ( 2 , 20 9 ) mean in the context of the problem?

  1. After 20 9 minutes, the height of the water is 2 centimeters less than at the start.
  2. After 2 minutes, the height of the water is 20 9 centimeters.
  3. After 20 9 minutes, the height of the water is 2 centimeters.
  4. After 2 minutes, the height of the water is 20 9 centimeters less than at the start.
  1. A scientist measures the height, h , of a tree each month, and m is the number of months since the scientist first measured the height of the tree. Is the height, h , a function of the month, m ?
  1. Yes
  2. No
  1. Cary started with 3 goldfish in her tank, and the population doubled every month. Which is an equation that represents the population, P , of goldfish after m months?
  1. P = 2 ⋅ 3 m
  2. P = 3 ⋅ 2 m
  3. P = 3 ( 2 m )
  4. P = 3 + 2 m

Use this equation for problems 7 – 10: f ( t ) = 50 ⋅ 2 t

  1. What is the initial value?
  1. What is the growth factor?
  1. What is the independent variable?
  1. f ( t )
  2. t
  1. What is the dependent variable?
  1. f ( t )
  2. t
  1. Which equation is most appropriate for modeling this data?
x 1 2 3 4 5 6
y 50 100 200 400 800 1600
  1. y = 50 ⋅ 2 1 x
  2. y = 25 ⋅ x 2
  3. y = 25 ⋅ 2 x
  4. y = 25 ⋅ ( 2 x ) 2