  ### Home > APCALC > Chapter 6 > Lesson 6.1.3 > Problem6-34

6-34.

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?

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

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.

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

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

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?

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?

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