22.1k views
0 votes
suppose california's population is 36.6 million people, and its population is expected to grow by 4% annually. how long will it take for the population to double? round your answer to the nearest whole number.

User Suresh D
by
8.9k points

1 Answer

5 votes

Final answer:

To calculate how long it will take for the population to double, we can use the formula for exponential growth. In this case, it will take about 18 years for California's population to double.

Step-by-step explanation:

To calculate how long it will take for the population to double, we can use the formula for exponential growth: P(t) = P(0) * (1 + r)^t, where P(t) is the population at time t, P(0) is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population is 36.6 million and the growth rate is 4%. We want to find the value of t when P(t) is double the initial population. Let's substitute the values into the formula and solve for t:

2 * 36.6 million = 36.6 million * (1 + 0.04)^t
Divide both sides by 36.6 million:
2 = (1.04)^t
Take the logarithm of both sides:
log(2) = t * log(1.04)
Divide both sides by log(1.04):
t = log(2) / log(1.04)

Using a calculator, we can find that t is approximately 17.67 years. Rounding to the nearest whole number, it will take about 18 years for the population to double.

Learn more about Exponential Growth

User Vbiqvitovs
by
8.1k points

No related questions found