The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Which countries have a decreasing populat

sibuzwaW

sibuzwaW

Answered question

2020-11-10

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=1193.1e0.006t
Country C A=36.5e0.017t
Country D A=121.7e0.005t
Country E A=145.3e0.004t

Answer & Explanation

Talisha

Talisha

Skilled2020-11-11Added 93 answers

Result used:
The exponential model is, A(t)=A0ekt
1. if k>0, the population is increasing.
2. if k<0, the population is decreasing
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=e0.005
ak=0.995011
ak=0.00498
Multiply -0.00498 with 100
ak=0.498%
ak0.5%
Obtain the decrease percent growth of E.
1+ak=e0.004
ak=0.996001
ak=0.00399
Multiply -0.00399 with 100.
ak=0.399%
ak0.4%
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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