the Museum of Science in Boston displays a running total of the U.S. population. on may 11, 1993, the total was increasing at the rate of 1 person every 14 sec. the displayed population figure at 3:45 PM. that day was 257,313,431. assume that the relative growth rate is constant.
A) what is the relative growth rate per year (365 days)?
B) at this rate, what will the U.S population be at 3:45 Pm Boston tiem in May 11, 2001
A) Compute the number of seconds in a year and divide it by 14. That will be the population increase. Express it as a percent of 257,313,431. I get 0.875%
B) 3:45 PM of May 11, 2001 is exactly 8 years later. Assume the annual growth rate stays the same in percentage terms. The 1993 population will have increased by a factor (1.00875)^8.
Don't assume my numbers are correct. Do the calculation yourself. which is 1.07222
A) To find the relative growth rate per year, we need to first calculate the number of seconds in a year. There are 365 days in a year and each day has 24 hours, 60 minutes, and 60 seconds.
So, the total number of seconds in a year = 365 days * 24 hours * 60 minutes * 60 seconds = 31,536,000 seconds.
The rate of increase is 1 person every 14 seconds. To find the relative growth rate per year, we need to calculate how many people would be added in a year at this rate:
Number of people added in a year = (31,536,000 seconds/year) / (14 seconds/person) = 2,252,571.43 people/year (rounded to the nearest whole person).
Therefore, the relative growth rate per year is approximately 2,252,571 people.
B) To calculate the future population at 3:45 PM Boston time on May 11, 2001, we need to determine the number of years between May 11, 1993, and May 11, 2001. That is 8 years.
Number of people added in 8 years = (8 years) * (2,252,571 people/year) = 18,020,568 people.
To find the future population, we add the number of people added in 8 years to the population on May 11, 1993:
Future population = 257,313,431 + 18,020,568 = 275,334,999 people.
Therefore, at 3:45 PM Boston time on May 11, 2001, the projected U.S. population would be approximately 275,334,999 people.
To find the relative growth rate per year, we need to determine how many seconds are in a year.
Step 1: Convert 365 days to seconds
365 days * 24 hours * 60 minutes * 60 seconds = 31,536,000 seconds
Step 2: Calculate the number of people added in a year
31,536,000 seconds / 14 seconds = 2,252,571.43 people
Step 3: Calculate the growth rate per year
Relative growth rate per year = Number of people added in a year / Population at a given time
Relative growth rate per year = 2,252,571.43 / 257,313,431 = 0.00875 (approximately)
Therefore, the relative growth rate per year is 0.00875.
Now let's calculate the U.S. population at 3:45 PM Boston time on May 11, 2001.
Step 4: Calculate the number of seconds between May 11, 1993, at 3:45 PM and May 11, 2001, at 3:45 PM
We need to find the time difference in seconds between these two dates.
For simplicity, let's assume there are 365 days in each year (ignoring leap years).
May 11, 1993, at 3:45 PM to May 11, 2001, at 3:45 PM is 8 years.
8 years * 31,536,000 seconds/year = 252,288,000 seconds
Step 5: Calculate the number of people added during this time period
252,288,000 seconds / 14 seconds = 18,020,571.43 people
Step 6: Calculate the projected U.S. population at May 11, 2001, at 3:45 PM
Projected U.S. population = Population at a given time + Number of people added during the time period
Projected U.S. population = 257,313,431 + 18,020,571.43 = 275,334,002.43 (approximately)
Therefore, at this rate, the projected U.S. population at 3:45 PM Boston time on May 11, 2001, would be approximately 275,334,002.