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Worksheet: Rates of Change in Populations

Q1:

A population’s size after 𝑑 days is given by 𝑓 ( 𝑑 ) = 1 1 𝑑 + 3 5 9 2 3 2 . Find the rate of change in the population when 𝑑 = 1 2 .

Q2:

The graph below shows the population of the country of Malawi over several decades starting from the year 1960.

What was the average rate of change, in millions per year, of the population between 1960 and 1970?

Which ten-year period witnessed the greatest rate of change of population?

  • Abetween 1980 and 1990
  • Bbetween 1990 and 2000
  • Cbetween 1970 and 1980
  • Dbetween 1960 and 1970
  • Ebetween 2000 and 2010

What constant annual rate of growth of the population, in millions per year, could account for the rise over the entire 56-year period?

Q3:

An account with an initial investment of $ 1 0 0 0 accrues interest at 4 . 2 5 % compounded continuously. The balance after 𝑑 years is modeled by 𝐴 = 1 0 0 0 𝑒 0 . 0 4 2 5 𝑑 . What is the average rate of change in the balance from 𝑑 = 1 to 2?