Question

in 2017, the estimated world population was 7.5 billion. use a doubling time of 45 years to predict the population in 2025, 2071, and 2119.

what will the population be in 2025?
the population will be 8.5 billion.
(round to one decimal place as needed.)

what will the population be in 2071?
the population will be billion.
(round to one decimal place as needed.)

Explanation:

Define the exponential growth model

Using the Exponential Growth and Doubling Time knowledge points:
The population \(P(t)\) after \(t\) years since 2017 is modeled by:

$$ P(t) = P_0 \cdot 2^{t / T_d} $$

where:

• \(P_0 = 7.5\) billion (population in 2017)
• \(T_d = 45\) years (doubling time)
• \(t = \text{Year} - 2017\)

Calculate the population in 2025

Using the Exponential Growth knowledge point:
For the year 2025, the elapsed time is:

$$ t = 2025 - 2017 = 8\text{ years} $$

Substitute \(t = 8\) into the model:

$$ P(8) = 7.5 \cdot 2^{8 / 45} \approx 7.5 \cdot 1.1311 \approx 8.483 $$

Rounding to one decimal place gives \(8.5\) billion.

Calculate the population in 2071

Using the Exponential Growth knowledge point:
For the year 2071, the elapsed time is:

$$ t = 2071 - 2017 = 54\text{ years} $$

Substitute \(t = 54\) into the model:

$$ P(54) = 7.5 \cdot 2^{54 / 45} = 7.5 \cdot 2^{1.2} \approx 7.5 \cdot 2.2974 \approx 17.23 $$

Rounding to one decimal place gives \(17.2\) billion.

Answer:

Question 1

What will the population be in 2025?

The population will be <blank>8.5</blank> billion.
(Round to one decimal place as needed.)

Question 2

What will the population be in 2071?

The population will be <blank>17.2</blank> billion.
(Round to one decimal place as needed.)