Question 1010384
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.