SOLUTION: 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=2

Question 1010384: 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 a decreasing population? By what percentage is the population of that country decreasing each year?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula with the negative exponent is modelling a decrease.

that formula is the formula for russia, which is a = 142.9e^-.004t.

the general formula is a = p * e^rt

r is the growth rate per time period
t is the number of time periods
a is the future value
p is the present value

t = 0 when the year is 2006.

in 2006, russia had 142.9 * e^(-.004*0) = 142.9 million people.

in 2007, russia has 142.9 * e^(-.004*1) = 142.3295417 million people.

to translate from continuous compounding to annual compounding, use the following formula.

(1+ar) = e^(cr)

ar is the annual compounging rate.
cr is the continuous compounding rate.

when cr = -.004, the formula becomes:

(1+ar) = e^-.004)

this results in (1+ar) = .9960079893

to solve for ar, subtract 1 form both sides of the equation to get:

ar = -.0039920107

the annual compounding rate is -.0039920107.

multiply this by 100 to get an annual compounding rate percent of -.39920107%.

this means the russian population is decreasing by .39920107% per year rounded to 8 decimal places.

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