A city of 2,950,000 people has a 2.5% annual decrease in population. Determine the city's population after 4 years.
population after 4 years = 2950000(0.975)^4
= 2665879
or to the nearest 1000, 2667000
the total decrease in population during fir5st year= 2950,000*2.5/100=73750
therefore, total decrease in population for 1 st year=2950,000-73750=2876250
total population in second year= 2876250
total decrease in population during the second year= 2876250*2.5/100=71906.25
therefore total decrease in population in second year=2876250-71906.25=2804343.8
total population for 3 rd year=2804343.8
total decrease in population in 3 rd year= 2804343.8*2.5/100=70108.594
therefore, total decrease in 3rd year=2804343.8-70108.594=2734235.2
total population for the fourth year=2734235.2
total decrease in population for fourth year=2734235.2*2.5/100=68355.88
total population decrease in fourth year=2734235.2-68355.88=2665879.3
thus correcting it to the nearest 1000 makes it 2,666,000
To determine the city's population after 4 years with a 2.5% annual decrease, you can follow these steps:
Step 1: Calculate the annual decrease.
Population decrease = 2.5% of 2,950,000
To calculate 2.5% of 2,950,000, we multiply 2,950,000 by 0.025:
Population decrease = 0.025 * 2,950,000
Step 2: Calculate the population after 1 year.
Population after 1 year = Current population - Population decrease
Population after 1 year = 2,950,000 - (0.025 * 2,950,000)
Step 3: Calculate the population after 2 years.
Population after 2 years = Population after 1 year - Population decrease
Population after 2 years = (2,950,000 - (0.025 * 2,950,000)) - (0.025 * 2,950,000)
Step 4: Calculate the population after 3 years.
Population after 3 years = Population after 2 years - Population decrease
Population after 3 years = ((2,950,000 - (0.025 * 2,950,000)) - (0.025 * 2,950,000)) - (0.025 * 2,950,000)
Step 5: Calculate the population after 4 years.
Population after 4 years = Population after 3 years - Population decrease
Population after 4 years = (((2,950,000 - (0.025 * 2,950,000)) - (0.025 * 2,950,000)) - (0.025 * 2,950,000)) - (0.025 * 2,950,000)
Simplifying the equation above will give us the population after 4 years.
To determine the city's population after 4 years, we need to calculate the decrease in population each year and subtract it from the initial population.
Step 1: Find the decrease in population each year.
The annual decrease is 2.5%, which is equivalent to 0.025 as a decimal. To find the decrease in population for each year, we multiply the initial population by this percentage.
Decrease in population = 0.025 * 2,950,000
Step 2: Calculate the population after 1 year.
To find the population after 1 year, we subtract the decrease in population from the initial population.
Population after 1 year = 2,950,000 - (0.025 * 2,950,000)
Step 3: Calculate the population after 2 years.
To find the population after 2 years, we repeat the same calculation as in step 2, but using the population after 1 year as the new initial population.
Population after 2 years = (Population after 1 year) - (0.025 * Population after 1 year)
Step 4: Repeat steps 2 and 3 for the remaining 2 years.
Population after 3 years = (Population after 2 years) - (0.025 * Population after 2 years)
Population after 4 years = (Population after 3 years) - (0.025 * Population after 3 years)
Now we can substitute the values into the equations to calculate the population after each year.