In 2010, the population of a town was 8500. The population decreased by 4.5% each year.
(a) Write an equation to find the population of the town t years after 2010.
(b) In what year will the population of the town be 7000?
Can anyone help me please I would appreciate it very much?
(a) P = 8500 * 0.955^t
(b) 4.217 years after 2010.
(a) Since the population decreases by 4.5% per year that means that 100% - 4.5% = 95.5% of the population is retained each year. So the equation becomes:
P = 8500 * 0.955^t
where
P = Population
t = number of years since 2010
(b) Just set the equation equal to 7000 and solve. So
P = 8500 * 0.955^t
7000 = 8500 * 0.955^t
7000 = 8500 * 0.955^t
0.823529412 = 0.955^t
log(0.823529412) = log(0.955^t)
log(0.823529412)/log(0.955) = t
-0.084320886/(-0.019996628) = t
4.216755142 = t
So the population of the town will be 7000 4.217 years after 2010.
