MCR 3UIExponential Growth & DecayWorksheet

  1. How many different pizzas can be created if 7 toppings are available.
  1. A chain letter has been sent to 4 friends and they are required to send the letter to 4 friends each and so on. How many letters are sent during round 5?
  1. The population of rabbits in MapletonCounty is growing at a rate of 13.5% per year. If there is a current population estimated at about 1500, how many will there be in 10 years?
  1. If the value of a laptop computer depreciates at 20% per year, how much will a $900 laptop be worth in 5 years?
  1. The population of Maryborough is currently 10 500. It has been growing at 7.5%/year. If this rate of growth continues, what will the population be in 25 years?
  1. A new Ferrari, fully loaded sells at $300 000, but depreciates at 13%/year. How much will it be worth used after 10 years?
  1. The population of a colony of bacteria doubles every 4 hours. The current population is 1000. Determine the population in :

a) 1 dayb) 18 hoursc) 24 hours ago.

  1. The half-life of caffeine in the bloodstream of an 8 year old child is approximately 2.5 hours. If Joey (8) eats a chocolate bar containing 110 mg of caffeine, how much caffeine is left in his bloodstream after:

a)5 hoursb) 12 hoursc) 1 day.

  1. When a basketball is correctly inflated it rebounds to approximately 60% of the height from which it is dropped. If a correctly inflated basketball is dropped from a height of 2.2m and continues to bounce each time rebounding to 60% of its height. Determine the height after 5 rebounds.
  1. Write as an exponential function base 2.

a) b) c)

  1. Describe the transformations to the graph of that results in :

a) b) c)

d) e) f)

12. The world population is doubling about every 35 years. In 1980 the total population was about 4.5 billion. If the doubling period remains at 35, find the projected world population for the year 2120.

  1. Five million bacteria live in an organism. The doubling period is 1.5 hours. State the number of bacteria after t hours, 9 hours and 1 day respectively.
  1. A bacterial culture doubles every 15 minutes. At 75 minutes an estimate of 40 000 is taken. Determine the:

a) initial size of the culture,

b) the culture size after 2 hours,

c) the culture size after 3 hours.

  1. An isotope of Sodium, Na, has a half-life of 15 hours. Determine the amount remaining from a 4 gram sample after:

a) 30 hoursb) t hoursc) 5 days.

  1. The half-life of Palladium-100, Pd, is 4 days. After 16 days a sample of Pd has been reduced to a mass of 0.75 grams. Determine the:
  2. initial mass of the sample
  3. mass of the sample after 2 days
  4. mass of the sample after 2 weeks.

ANSWERS

1. 128 2. 10243. 53224. 294.915. 64 033

6. $74 527.02 7. a) 64 000b) 22 627c) 16

8.a) 27.5mgb) 3.95mg c) 0.14mg9. 17cm

10a) b) c)

11.a) Translation right 4 and up 6

b) Reflection in x-axis, Translation left 1 and down 2

c) Vertical stretch by 2, reflection in y-axis, Translation right 2 and down 7

d) Vertical stretch by 4, reflection in y-axis, Translation left 1 and up 5

e) Horizontal compression by 2, Translation left 2

f) Reflection in y-axis

12. 72 billion13a) b) c)

14.a) 1250b) 320000c) 5120000

15. a) 1gb) c) 0.015625 g

16.a) 12gb) 8.5gc) 1.1 g