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Lesson: Exponential Growth

Worksheet: Exponential Growth • 12 Questions


A mathematical model predicts that the population of a city, million, will be given by the formula , where is the number of years from now. What does the model predict the population will be in 2 years’ time?


A bacterial colony’s population doubles every 5 hours. How long does it take to triple? Give the result to the nearest one decimal place.


David has 73 rabbits. He believes that he will have rabbits after months. How many rabbits does he expect to have 2 months from now?

  • A634 rabbits
  • B191 rabbits
  • C635 rabbits
  • D200 rabbits


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


A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees. To the nearest year, how long ago was the wood for the artifact cut from the tree? Note that the half-life of carbon-14 is 5 730 years.


A microorganism reproduces by binary fission, where every hour each cell divides into two cells. Given that there are 24 431 cells to begin with, determine how long it will take for there to be 97 724 cells.


At the end of 2000, the population of a country was 22.4 million. Since then, the population has increased by every year. What is the population, rounded to the nearest tenth, of the country at the end of 2037?


Which graph demonstrates exponential growth?

  • A
  • B
  • C
  • D


The population of a city is growing according to the equation , where is the population in millions, and is the number of years since 2015. What was the population of the city in 2015?


In 1970, the world population was 3.682 billion and showed a growth rate of per year. Assuming a constant growth rate, what would have been the estimate for the size of the population in 2017? Give your answer accurate to four significant figures.

  • A9.89 billion
  • B8.119 billion
  • C9.689 billion
  • D4.059 billion
  • E9.787 billion


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


The population of Malawi, in millions, between 1960 and 2016 can be modeled by the function . By how much has the average rate of growth changed from the period 1960 to 1965 to the period 2011 to 2016? Give your answer in thousands per year to the nearest thousand.

  • A
  • B
  • C
  • D
  • E