The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year? Country B A=1193.1e^{0.006t} Country C A=36.5e^{0.017t} Country D A=121.7e^{-0.005t} Country E A=145.3e^{-0.004t}

Question
Exponential models
asked 2021-01-23
The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?
Country B \(A=1193.1e^{0.006t}\)
Country C \(A=36.5e^{0.017t}\)
Country D \(A=121.7e^{-0.005t}\)
Country E \(A=145.3e^{-0.004t}\)

Answers (1)

2021-01-24
Result used:
The exponential model is, \(A(t)=A_0e^{kt}\)
1. if k>0, the population is increasing.
2. if k
From the given four countries, it is observed that the countries D and E only have the negative k values.
Thus, Country D and Country E have the decreasing populations.
Use the formula (1 +ak) to convert the continuous compound growth to annual compound growth.
Obtain the decrease percent growth of D.
\(1+ak=e^{-0.005}\)
\(ak=0.99501-1\)
\(ak=-0.00498\)
Multiply -0.00498 with 100
ak=-0.498%
\(ak\approx-0.5\%\)
Obtain the decrease percent growth of E.
\(1+ak=e^{-0.004}\)
\(ak=0.99600-1\)
\(ak=-0.00399\)
Multiply -0.00399 with 100.
\(ak=-0.399\%\)
\(ak\approx-0.4\%\)
Thus, the population of Country D is decreasing by 0.5% and the popualtion of country E is decreasing by 0.4% each year.
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