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Algebra 1

5.7.5 Practice

Algebra 15.7.5 Practice
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Complete the following questions to practice the skills you have learned in this lesson.

  1. The two graphs show models characterized by exponential decay representing the area covered by two different algae blooms, in square yards, w weeks after different chemicals were applied.

    Graph of two functions on grid.

    Which algae bloom covered a larger area when the chemicals were applied?

  1. The algae bloom represented by the circles because the curve is always below the other one on the graph.
  2. Both algae blooms covered the same area after 5 weeks.
  3. The algae bloom represented by the circles because the curve has a lower y -intercept.
  4. The algae bloom represented by the triangles because the curve has a higher y -intercept.
  1. The two graphs show models characterized by exponential decay representing the area covered by two different algae blooms, in square yards, w weeks after different chemicals were applied.

    Graph of two functions on grid.

    Which algae population is decreasing more rapidly? Explain how you know.

  1. The algae bloom represented by the triangles because its graph is steeper.
  2. The algae bloom represented by the circles because the curve is always below the other one on the graph.
  3. Both algae blooms are decreasing at the same rate.
  4. The algae bloom represented by the triangles because the curve has a higher y -intercept.
  1. A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown in the graph.

    Graph of a function on grid.

    What fraction of the burn area remains each week?

  1. 2 3 or .66
  2. 1 4 or .25
  3. 3 4 or .75
  4. 1 2 or .5
  1. A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown in the graph.

    Graph of a function on grid.

    Which of the following is an equation representing the area of the burn, a , after t weeks?

  1. a = − 6 5 t + 8
  2. a = − 2 t + 8
  3. a = 8 ( 3 4 ) t
  4. a = 8 ( 1 4 ) t
  1. A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown in the graph.

    Graph of a function on grid.

    What is the area of the burn after 7 weeks? Round to three decimal places.

  1. The graphs show the amounts of medicine in two patients after receiving injections. The circles show the medicine in patient A, and the triangles show the medicine in patient B.

    Two functions plotted on the same grid.

    One equation that gives the amount of medicine in milligrams, m , in patient A, h hours after an injection, is m = 300 ( 1 2 ) h .

    What could be an equation for the amount of medicine in patient B?

  1. m = 200 ( 7 10 ) h
  2. m = 200 ( 3 10 ) h
  3. m = 500 ( 7 10 ) h
  4. m = 500 ( 3 10 ) h
  1. Which scenario could describe the graph?


    GRAPH OF AN INCREASING EXPONENTIAL FUNCTION WITH A \(y\)-intercepts OF 10 AND PASSING THROUGH THE POINTS (1, 20) AND (2, 40).;

  1. A population of bacteria starts with 200 and decays by a factor of 1 2 every hour.
  2. A population of bacteria increases by a factor of 10 every hour and starts with 2 bacteria.
  3. A savings account starts with $200 and decays by a factor of 1 2 each month.
  4. A population of bacteria doubles every hour and starts with 10 bacteria.
  1. Which equation could represent the graph?


    SCATTER PLOT THAT CAN BE MODELED BY AN INCREASING EXPONENTIAL FUNCTION WITH A \(y\)-intercepts THAT IS SLIGHTLY MORE THAN 2. THE SCATTER PLOT INCLUDES A POINT WITH AN X-VALUE OF 1 AND A Y-VALUE OF APPROXIMATELY 3-POINT-1, A POINT WITH AN X-VALUE OF 2 AND A Y-VALUE OF APPROXIMATELY 4-POINT-6, AND A POINT WITH AN X-VALUE OF 3 AND A Y-VALUE OF APPROXIMATELY 6-POINT-8.;

  1. y = .479 ( 2.104 ) x
  2. y = 2.104 ( .479 ) x
  3. y = 2.5 x + 2
  4. y = 2.104 ( 1.479 ) x
  1. Given a formula for an exponential function, is it possible to determine whether the function grows or decays exponentially just by looking at the formula? Explain.
  1. No, it is not possible to determine growth and decay from the formula.
  2. Yes, if the growth rate is greater than one it’s growth; if the growth rate is, less than zero it’s decay.
  3. Yes, if the growth rate is between zero and one it’s decay; if the growth rate is greater than one it is growth.
  4. Yes, if the initial value is greater than one it’s growth; if the initial value is less than one it’s decay.
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