Step 1 :We are given two data points: (0, 20) and (10, 23.7), where the first number in the pair is the number of years since 1970 and the second number is the population in millions. We are asked to find an exponential growth model, which has the form \(P(t) = P_0 * e^{kt}\), where \(P_0\) is the initial population, \(k\) is the growth rate, and \(t\) is time. We can use the two data points to solve for \(P_0\) and \(k\).
Step 2 :From the given data, we can see that the initial population \(P_0\) is 20 million.
Step 3 :We can use the second data point (10, 23.7) to solve for \(k\). Substituting \(P_0 = 20\), \(t = 10\), and \(P(t) = 23.7\) into the exponential growth model, we get \(23.7 = 20 * e^{10k}\). Solving this equation for \(k\), we get \(k = 0.01697\).
Step 4 :Now we can write the exponential growth model as \(P(t) = 20 * e^{0.01697t}\). This model can be used to predict the population of California at any given year since 1970.
Step 5 :\(\boxed{P(t) = 20 * e^{0.01697t}}\) is the exponential growth model for the population of California.