Final answer:
To estimate the average world population from 1950 to 1980 using the provided model, calculate the populations in 1950 and 1980, then find the average and round to the nearest million. This demonstrates the dynamic nature of world population growth and the implications for population modeling.
Step-by-step explanation:
To estimate the average world population from 1950 to 1980 using the given exponential model p(t) = 2,560e0.017185t, you need to first calculate the population at the beginning and end of the time period using the value of t that represents the number of years since 1950. So for 1950, t = 0, and for 1980, t = 30.
To find the population in 1950, substitute t = 0 into the equation:
p(0) = 2,560e0.017185(0) = 2,560e0 = 2,560 million people
To find the population in 1980, substitute t = 30 into the equation:
p(30) = 2,560e0.017185(30)
You would then calculate p(30) using a calculator or computer to find the population in 1980. To find the average population over the 30 years, you add the starting population to the ending population, divide by 2, and round to the nearest million.
The world population growth has been quite dynamic over the last century. During the 20th century, there was a significant decrease in death rates and an increase in birth rates, leading to exponential growth. The average growth rates over different time periods have implications for how population dynamics are modeled and predicted.
It is important to note that actual historical rates of growth have varied, with the model in the question reflecting the conditions pertinent to the second half of the 20th century.