Question

complete the table shown to the right for the population growth model for a certain country.
2004
population(millions) 85.5
projected 2029
population (millions)
projected
growth rate, k 0.0104
the projected 2029 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 time \( t \).

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

• \( P_0 = 85.5 \) million (population in 2004)
• \( k = 0.0104 \) (projected growth rate)
• \( t = 2029 - 2004 = 25 \) years (time elapsed from 2004 to 2029)

Step3: Substitute the values into the formula

First, calculate \( kt \): \( kt = 0.0104 \times 25 = 0.26 \)

Then, calculate \( e^{kt} \): \( e^{0.26} \approx 1.3001 \) (using a calculator for the exponential function)

Now, calculate \( P \): \( P = 85.5 \times 1.3001 \approx 111.15855 \)

Step4: Round to one decimal place

Rounding \( 111.15855 \) to one decimal place gives \( 111.2 \)

Answer:

111.2