World population Human population growth rates vary geographicallyand fluctuate over time. The overall growth rate for world population peaked at an annual rate of 2.1% per year in the 1960s. Assume a world population of 6.0 billion in 1999 (t = 0) and 7.4 billion in 2017 (t = 18).a. Find an exponential growth function for the world population that fits the two data points.b. Find the doubling time for the world population using the model in part (a).c. Find the (absolute) growth rate y'(t) and graph it, for 0 ≤ t ≤ 50.d. According to the growth model, how fast is the population expected to be growing in 2020 (t = 21)?
World population Human population growth rates vary geographically
and fluctuate over time. The overall growth rate for world population peaked at an annual rate of 2.1% per year in the 1960s. Assume a world population of 6.0 billion in 1999 (t = 0) and 7.4 billion in 2017 (t = 18).
a. Find an exponential growth function for the world population that fits the two data points.
b. Find the doubling time for the world population using the model in part (a).
c. Find the (absolute) growth rate y'(t) and graph it, for 0 ≤ t ≤ 50.
d. According to the growth model, how fast is the population expected to be growing in 2020 (t = 21)?
“Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”
Solving first three parts:
a) Exponential population growth function can be represented by :
where t is the no. of years and k is the growth constant and is the population at t=0
Hence,
For t=0
Thus,
Hence,
When t=18,
The equation for the exponential population can be determined by :
Hence,
Taking Logarithm both sides:
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