Question

This exercise uses the population growth model. The population of California was 10,586,223 in 1950 and 23,668,562 in 1980. Assume the population grows exponentially. Find a function that models the population t years after 1950.

Answer 1

To model the population t years after 1950, we can use the exponential growth formula. Calculating the growth rate, we can determine the function that represents the population. Therefore, the function that models the population t years after 1950 is P(t) = 10,586,223 * e^(0.0236*t).

Step-by-step explanation:

To find a function that models the population t years after 1950, we can use the exponential growth formula:

P(t) = P0 * e(r*t)

Where P(t) represents the population at time t, P0 represents the initial population, r represents the growth rate, and e represents Euler's number (approximately 2.71828).

Using the given information, we have:

P(0) = 10,586,223 (in 1950)

P(t) = 23,668,562 (in 1980)

Let's calculate the value of r:

23,668,562 = 10,586,223 * e(r*(1980-1950))

Simplifying, we have:

2.234 = e(30r)

Taking the natural logarithm of both sides, we get:

ln(2.234) = 30r

Now, we can solve for r:

r = ln(2.234)/30

r ≈ 0.0236

Therefore, the function that models the population t years after 1950 is:

P(t) = 10,586,223 * e(0.0236*t)