Question

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?

Answer 1

(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.