Question 1010383: Directions: The exponential models describe the population of the indicated country, A, in millions, t years after 2006. Use these models to solve. India A=1095.4e^0.014t Iraq A=26.8e^0.027t Japan A= 127.5e^0.001t Russia A=142.9e^-0.004t
Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general formula for continuous compounding is:
A = p * e^(rt)
A is the future value
p is the present value
r is the continuous compounding growth rate per time period.
t is the numbe of time periods.
the time periods for this problem are expressed in years.
the country with the highest value of r has the highest continuous compounding growth rate.
that country would be iraq with a continuous compounding growth rate of .027 per year.
to convert from continuous compounding growth rate to annual compounding growth rate, use the following formula.
(1+ar) = e^cr
when cr = .027, that formula becomes:
(1+ar) = e^.027 = 1.027367803
to solve for ar, subtract 1 from both sides of the equation to get:
ar = .027367803.
that's the annual compounding growth rate.
the annual compounding growth rate percent is equal to 2.7367803%.
the population in iraq is growing at a rate of 2.7367803% per year.
since the formulas are equivalent, they should yield the same result.
using continuous compounding formula for 1 year:
26.8 * e^.027 = 27.53345711
using annual compounding formula for 1 year:
26.8 * (1.027367803) = 27.53345711
they're the same, confirming that the two formulas are equivalent.
the annual growth rate for all of the countries is shown below:
india:
e^.014 = 1.014098459 - 1 = .014098459 = 1.4098459%
iraq:
e^.027 = 1.027367803 - 1 = .027367803 = 2.7367805%
japan:
e^.001 = 1.0010005 - 1 = .0010005 = 1.0005%
russia:
e^-.004 = .9960079893 - 1 = -.0039920107 = -.39920107%
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