The population of Las Vegas, Nevada in 2000 was 478,000 and is increasing at the rate of 6.28% per year. At this rate, when will the population reach 1 million people?
Impossible question.
Considering that Las Vegas's population has considerably shrunk due to the recession, this question makes no sense today.
The 2010 population was 583,756
http://en.wikipedia.org/wiki/Las_Vegas,_Nevada
To determine when the population of Las Vegas will reach 1 million people, we can use the concept of compound interest since the population is increasing by a constant percentage each year. Here's how you can calculate it step by step:
Step 1: Calculate the annual growth rate as a decimal by dividing the percentage growth rate by 100:
Annual growth rate = 6.28% / 100 = 0.0628
Step 2: Determine the initial population in 2000:
Initial population = 478,000
Step 3: Set up the exponential growth formula where P is the expected population and t is the number of years since 2000:
P = Initial population * (1 + Annual growth rate)^t
Step 4: Plug in the values and solve for t (the number of years):
1,000,000 = 478,000 * (1 + 0.0628)^t
Step 5: Divide both sides of the equation by 478,000 to isolate the exponential term:
1,000,000 / 478,000 = (1 + 0.0628)^t
Step 6: Take the natural logarithm (ln) of both sides of the equation to remove the exponential term:
ln(1,000,000 / 478,000) = ln((1 + 0.0628)^t)
Step 7: Simplify the equation using the properties of logarithms:
ln(2.091 = t * ln(1.0628)
Step 8: Divide both sides of the equation by ln(1.0628) to solve for t:
t = ln(2.091) / ln(1.0628)
Step 9: Use a calculator or a programming language to solve for t:
t ≈ 25.35
Therefore, the population of Las Vegas, Nevada will reach 1 million people around 25-26 years after 2000.