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How Do You Solve a Word Problem with Exponential Growth?

In 2000, the population of the town of Nerdville was 100 people. Since then, the population has increased at a constant rate of 30% each year. Assuming this rate of increase stays constant, what will the population of Nerdville be in 2020?

Summary

  1. Increasing by a constant RATE means we have an exponential function
  2. Increasing by a constant AMOUNT would mean we would have a linear function
  3. To find the time in years, subtract the initial year from the ending year

Notes

    1. The formula for exponential growth is f(t) = a(1+r)t
    2. 'a' is the initial amount
    3. 'r' is the rate of increase
    4. 't' is the time in years
    5. 'a' and 'r' must both be greater than 0
    1. The formula for exponential growth is f(t) = a(1+r)t
    2. 'a' is the initial amount
    3. 'r' is the rate of increase
    4. 't' is the time in years
    1. To convert a percent to a decimal, drop the percent symbol and move the decimal point two places to the left
    2. So 30% becomes 0.3
    1. Plug in 100 for 'a', 0.3 for 'r', and 20 for 't' into f(t) = a(1+r)t
    2. This gives us f(20) = 100(1+0.3)20
    1. Use the order of operations to simplify the right hand side
    2. First simplify inside the parentheses
    3. Then evaluate the exponent
    4. Then multiply what's left
    5. Since we're looking for a population of people, we need to drop the decimal off the end of the answer we get