Final answer:
The calculation involves forming an exponential growth equation to determine the doubling time of California's population from 1950 to 1980, which can be calculated using methods such as the rule of 70 or by solving for the growth rate in the exponential growth formula.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with exponential growth and population models. The grade level is High School. To find the time required for the population of California to double, we can use the population growth formula, based on exponential growth.
First, we identify that the population in 1950 was 10,586,223, and by 1980, it grew to 23,668,562. To calculate the doubling time, we can use the rule of 70, which is a way to estimate the number of years required to double the population at a constant annual growth rate. However, we can also use a more accurate method by setting up an exponential equation:
P(t) = P0 * e(rt)
Where:
P(t) is the population at time t,
P0 is the initial population,
r is the growth rate,
t is the time in years, and
e is Euler's number (approximately 2.71828).
We can use the given populations from 1950 and 1980 to solve for the growth rate r and then solve for t to find the doubling time.