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Worksheet: Exponential Growth and Decay

Q1:

The population, 𝑁 , of a city in year 𝑑 is given by the formula 𝑁 = 1 0 ( 2 . 6 ) 4 𝑑 βˆ’ 2 0 0 1 . Determine the year in which the population of the city was 8 million.

Q2:

The population, 𝑁 , of a city in year 𝑑 is given by the formula 𝑁 = 1 0 ( 3 . 8 ) 4 𝑑 βˆ’ 2 0 0 2 . Determine the year in which the population of the city was 2.1 million.

Q3:

Jacob invests in a savings account. After ten years, the value of his investment had doubled. What was the annual rate of interest? Give your answer to one decimal place.

Q4:

A population of bacteria in a petri dish 𝑑 hours after the culture has started is given by 𝑃 = 2 4 0 0 β‹… 𝑒 0 . 0 8 4 𝑑 . Emma says this means that the growth rate is 8 . 4 % per hour. Her friend Jennifer, however, says that the hourly growth rate is 8 . 7 6 % . Who is right?

  • AJennifer
  • BEmma

Q5:

The value of a car falls by 3 6 % over 2 years. By considering a suitable exponential function, find the equivalent annual rate of depreciation that would produce the same fall in value over two years.

Q6:

The given figure shows the concentration 𝑐 , in micrograms per liter, of a certain drug in human blood plasma measured at different times. Considering that the concentration after β„Ž hours can be modeled with the function 𝑐 = 1 8 β‹… 0 . 7 5 β„Ž , by what percentage does the drug’s concentration decrease every hour?

  • A 5 0 %
  • B 7 5 %
  • C 1 5 %
  • D 2 5 %
  • E 1 0 %

Q7:

A car’s value depreciates by π‘Ÿ % every year. A new car costs 𝑃 dollars.

Write a function that can be used to calculate 𝑉 , the car’s value in dollars, after 𝑑 years.

  • A 𝑉 ( 𝑑 ) = 𝑃 ο€» π‘Ÿ 1 0 0  𝑑
  • B 𝑉 ( 𝑑 ) = 𝑃 ο€» 1 + π‘Ÿ 1 0 0  𝑑
  • C 𝑉 ( 𝑑 ) = ο€» 1 βˆ’ π‘Ÿ 1 0 0  𝑑
  • D 𝑉 ( 𝑑 ) = 𝑃 ο€» 1 βˆ’ π‘Ÿ 1 0 0  𝑑
  • E 𝑉 ( 𝑑 ) = ο€» 𝑃 βˆ’ π‘Ÿ 1 0 0  𝑑

What is the value of π‘Ÿ for which the car’s value will be halved in 3 years? Give your answer to the nearest whole number.