The exponential models the population of the indicated country, A, in millions, t years after 20006. Which country has the greatest growth rate? By wh

Jaya Legge

Jaya Legge

Answered question

2021-02-06

The exponential models the population of the indicated country, A, in millions, t years after 20006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
Country 1: A=26.3e0.029t
Country 2: A=127.7e0.007t
Country 3: A=148.5e0.0091t
Country 4: A=1094.2e0.016t

Answer & Explanation

Caren

Caren

Skilled2021-02-07Added 96 answers

Given:
The exponential model that describe the population of different countries:
Country 1: A=26.3e0.029t
Country 2: A=127.7e0.007t
Country 3: A=148.5e0.0091t
Country 4: A=1094.2e0.016t
Population growth is equal to differentiation of exponential model with respect to ‘t’,
So now differentiating the given function one by one:
ddt(A1)=ddt(26.3e0.029t)
dA1dt=(26.3×0.029e0.029t)
dA1dt=(0.7627e0.029t)
ddt(A2)=ddt(127.7e0.007t)
dA1dt=(127.7×0.007e0.007t)
dA1dt=(0.8939e0.007t)
ddt(A3)=ddt(148.5e0.009t)
dA3dt=ddt(148.5×(0.009)e0.009t)
dA3dt=(1.3365e0.009t)
ddt(A4)=ddt(1094.2e0.016t)
dA4dt=ddt(1094.2×0.016e0.016t)
dA4dt=(17.5072e0.016t)
To check which one is larger, by comparing the quantities of growth rate it can be concluded that:
Country 4: A4=1094.2e0.016t
Has the greates growth rate.
To find the percentage change in population:
Country 4: A4=1092.2e0.016t
Now put t=0,
A4=1094.2e0.016×0
A4=1094.2e0
A4=1094.2
Now put t=1,
A4=1094.2e0.016×1
A4=1094.2e0.016
A4=1111.8
Now,
Percentage change =1111.81094.21094.2×100
Percentage change =1.60
Answer: The final answer is given below:
Country 4: A=1094.2e0.016t
Has the greates growth rate.
Percentage change in population each year =1.60

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