Question

complete the table shown to the right for the population growth model for a certain country.
2003 \tpopulation(millions) \t87.5
projected 2038 \tpopulation (millions) \t
projected \tgrowth rate, k \t0.0087
the projected 2038 population is square million.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the formula for population growth

The formula for exponential population growth is \( P = P_0 e^{kt} \), where \( P_0 \) is the initial population, \( k \) is the growth rate, \( t \) is the time in years, and \( P \) is the population after \( t \) years.

Step2: Determine the values of \( P_0 \), \( k \), and \( t \)

• \( P_0 = 87.5 \) million (population in 2003)
• \( k = 0.0087 \) (projected growth rate)
• \( t = 2038 - 2003 = 35 \) years (time from 2003 to 2038)

Step3: Calculate the exponent \( kt \)

\( kt = 0.0087 \times 35 = 0.3045 \)

Step4: Calculate \( e^{kt} \)

Using a calculator, \( e^{0.3045} \approx 1.356 \) (rounded to three decimal places for accuracy)

Step5: Calculate the projected population \( P \)

\( P = 87.5 \times 1.356 \approx 118.65 \)

Step6: Round to one decimal place

\( 118.65 \) rounded to one decimal place is \( 118.7 \)

Answer:

118.7