In the year 2000, the United States had a population of about 281.4 million people; by 2010, the population had risen to about 3 08.7 million.
Part A
Find the 10-year continuous growth rate using P=
.
Part B
Write an equation to model the population growth of the United States, and use it to estimate the population in 2020.
1 answer:
Answer:
Part 1. 0.9259 % per year
Part 2. P = 281.4e^(0.009 259t); 338.6 million
Step-by-step explanation:
Data:
P₀ = 281.4 million
P = 308.7 million
Part 1. Growth rate
t = 2010 - 2000 = 10 yr
P = P₀e^(rt)
308.7 = 281.4e^(10r)
e^(10r) = 1.0970
10r = ln1.0970
r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259
r = 0.9259 % per year
The 10-year continuous growth rate is 0.9259 % per year.
Part 2. Population model
The population model is
P = 281.4e^(0.009 259t)
where P is in millions and t is the number of years since 2000.
By 2020,
P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203
P = 338.6 million
The estimated population in 2020 is 338.6 million.
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