Question

score on last try: 0 of 3 pts. see details for more. next question get a similar question you can retry this question below the world population in the year 1998 was 5.964 billion people, with an annual growth rate of 1.2826%. assume that world population can be modelled as an exponential function with a constant growth rate, and estimate the population in the year 2017 to three decimals: population in year 2017 = billion people note: annual population growth fluctuates according to economic, demographic, and geopolitical trends. it is rarely constant! the actual population in the year 2017 was 7.509 billion, which reflects the slowing growth rate of world population in the early 21st century. question help: video

Explanation:

Step1: Recall the exponential growth formula

The formula for exponential growth is \( P(t) = P_0 e^{rt} \), where \( P_0 \) is the initial population, \( r \) is the annual growth rate (in decimal), and \( t \) is the time in years.
First, convert the growth rate to decimal: \( r = 1.2826\% = 0.012826 \).
The initial population \( P_0 = 5.964 \) billion (in 1998), and we need to find the population in 2017. The time \( t = 2017 - 1998 = 19 \) years.

Step2: Substitute values into the formula

Substitute \( P_0 = 5.964 \), \( r = 0.012826 \), and \( t = 19 \) into the formula:
\( P(19) = 5.964 \times e^{0.012826 \times 19} \)
First, calculate the exponent: \( 0.012826 \times 19 \approx 0.243694 \)
Then, calculate \( e^{0.243694} \approx 1.275 \) (using a calculator for the exponential function)
Now, multiply by the initial population: \( 5.964 \times 1.275 \approx 7.604 \)

Answer:

\( 7.604 \)