Answer: To find the function Q(t) that expresses the world population (in billions) as a function of time t (in years), we can use the formula for exponential growth:
Q(t) = Q0 * (1 + r)^t,
where:
Q(t) is the world population at time t,
Q0 is the initial population at t = 0,
r is the growth rate per year (in decimal form),
t is the time in years.
Given that the world population at the beginning of 1990 (t = 0) was 5.3 billion, and the growth rate is 2.7% per year (in decimal form, r = 0.027), we can find the function Q(t):
Q(t) = 5.3 * (1 + 0.027)^t.
Now, let's complete the table of values for the years 1990, 1995, 2000, 2005, 2010, 2015, 2020, and 2025:
Year | t | Q(t)
1990 | 0 | 5.3
1995 | 5 | 5.3 * (1.027)^5
2000 | 10 | 5.3 * (1.027)^10
2005 | 15 | 5.3 * (1.027)^15
2010 | 20 | 5.3 * (1.027)^20
2015 | 25 | 5.3 * (1.027)^25
2020 | 30 | 5.3 * (1.027)^30
2025 | 35 | 5.3 * (1.027)^35
Now, let's calculate the values for each year using the function Q(t):
Q(5) ≈ 5.3 * (1.027)^5 ≈ 5.3 * 1.1397 ≈ 6.04 billion (rounded to one decimal place).
Q(10) ≈ 5.3 * (1.027)^10 ≈ 5.3 * 1.3121 ≈ 6.99 billion (rounded to one decimal place).
Q(15) ≈ 5.3 * (1.027)^15 ≈ 5.3 * 1.5117 ≈ 7.99 billion (rounded to one decimal place).
Q(20) ≈ 5.3 * (1.027)^20 ≈ 5.3 * 1.7410 ≈ 9.22 billion (rounded to one decimal place).
Q(25) ≈ 5.3 * (1.027)^25 ≈ 5.3 * 2.0054 ≈ 10.63 billion (rounded to one decimal place).
Q(30) ≈ 5.3 * (1.027)^30 ≈ 5.3 * 2.3117 ≈ 12.26 billion (rounded to one decimal place).
Q(35) ≈ 5.3 * (1.027)^35 ≈ 5.3 * 2.6673 ≈ 14.12 billion (rounded to one decimal place).
So, the completed table of values (rounded to one decimal place) is:
Year | t | Q(t)
1990 | 0 | 5.3
1995 | 5 | 6.0
2000 | 10 | 7.0
2005 | 15 | 8.0
2010 | 20 | 9.2
2015 | 25 | 10.6
2020 | 30 | 12.3
2025 | 35 | 14.1
The world population (in billions) for each respective year is given in the last column.