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Worksheet: Exponential Growth and Decay

Q1:

Several fish were accidentally released into a lake. After weeks, the number of fish is estimated to be . Determine the likely number of fish in the lake after 5 weeks. Give your answer to the nearest whole number.

  • A266
  • B95
  • C35
  • D325

Q2:

The function represents a population, in millions, years after 1970 that is growing at an annual rate of and started at 13.2 million in 1970. What is the value of ?

Q3:

A microorganism reproduces by binary fission, where every hour each cell divides into two cells. Given that there are 8 075 cells to begin with, determine how long it will take for there to be 516 800 cells.

Q4:

The population of a city increases by every year. How many years does it take for the population of the city to double?

Q5:

The population, , of a city in year is given by the formula . Determine the year in which the population of the city was 2.1 million.

Q6:

A doctor injected a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there were 4.75 milligrams of dye remaining in the patient’s system. Which of the following is an appropriate model for this situation?

  • A
  • B
  • C
  • D

Q7:

At the start of an experiment, a scientist has a sample which contains 250 milligrams of a radioactive isotope. The radioactive isotope decays exponentially, so that after 250 minutes there are only 32.0 milligrams of the isotope left.

Write the mass of isotope in milligrams, , as a function of the time in minutes, , since the experiment started. Give your answer in the form , rounding and to three significant figures.

  • A
  • B
  • C
  • D
  • E

Find the half-life of the isotope, giving your answer to the nearest minute.

  • A94 minutes
  • B76 minutes
  • C84 minutes
  • D122 minutes
  • E4 minutes

Q8:

A quantity decays in time years according to the formula . If half the amount is left after 46 years, what is the value of ?

  • A2
  • B
  • C
  • D
  • E

Q9:

Benjamin wants to save for a down payment on a home. How much will he need to invest in an account with APR, compounding daily, in order to reach his goal in 5 years?