According to the State Department of Finance, California’s population was $33.218$ million at the beginning of 1998, $33.765$ million at the beginning of 1999, and $34.336$ million at the beginning of 2000.

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

   Hint (a):

   $\text{Percent Increase} = \frac{(\text{new amount})-(\text{original amount})}{\text{original amount}}$

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

2. Assuming exponential population growth, write an equation to model this data.

   Hint (b):

   $P\left(t\right) = P_{0}\left(1 − \text{rate}\right)^{t}$
   Let the year 1998 correspond with $t = 0$.

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

   Hint (c):

   Evaluate $P\left(22\right)$.

4. The increase in population is proportional to the current population. In other words, if the population is growing $3\%$ each year and the current population is $1000$ people, the increase is $30$ people. If the current population is $5000$ people, the increase is $150$ people. According to your model, by approximately how many people did California’s population increase in the year 2000?

   Answer (d):

   Answers will vary depending on the rate estimate. $≈ 34,336,000\left(\text{rate}\right)$

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

   Hint (e):

   $\text{Approximate growth in population} = P_{0}\left(\text{growth factor}\right).$
   Find growth factor in part (a).