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6-34.
  1. According to the State Department of Finance, California's population was 33.218 million people at the beginning of 1998, 33.765 million at the beginning of 1999, and 34.336 million at the beginning of 2000. Homework Help ✎

    1. Find the percent increase from 1998 to 1999 and the percent increase from 1999 to 2000. Does this suggest exponential population growth?

    2. Assuming exponential population growth, find a model that approximately fits this data.

    3. Use your model to predict California's population in 2020 assuming your growth model remains valid.

    4. The increase in population is proportional to the current population. In other words, if the population is growing 3% each year, then if the population is 1,000 people, the increase is 30 people. If the population is 5,000 people, the increase is 150 people. Approximately how much should California's population have increased in the year 2000?

    5. Explain why the increase is proportional to the population. What is the constant of proportionality?

Calculate this value with the two different data sets. Are they nearly the same?

P(t) = P0(1 − rate)t
Let the year 1998 correspond with t = 0.

Evaluate P(22).

Answers will vary depending on the rate estimate. ≈ 34,336,000(rate)

Approximate growth in population = P0(growth factor).
Find growth factor in part (a).