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The world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at the rate of approximately 2.7%/year and find the function Q(t) that expresses the world population (in billions) as a function of time t (in years), with t = 0 corresponding to the beginning of 1990. Using this function, complete the following table of values. (Round your answers to one decimal place.)

1990
1995
2000
2005
2010
2015
2020
2025

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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.

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