Question

A town hasapopulation of p people based on a 2010 census. According to research conducted by the town council, the population of the city is expected to increase by 5 percent per year. According to the estimate, the expected population of the town in 2020 is 810. To the nearest whole number, what is the value of p ?

Answer 1

p = 497 ( to the nearest whole number)

Explanation:

In order to do this calculation, we will apply the principle of accounting, where a certain amount is compounded periodically and yielding a future value. Compound interest is used because the percentage growth rate is added on the new amount gotten each year, and not on the first or original amount.

Hence:

FV = PV ×
`(1+ (r)/(n)) ^(n*t)`

where FV = future value = population in 2020 = 810

PV = present value = population in 2010 = p

r = percentage growth rate in decimal = 5% = 5/100 = 0.05

n = growth rate period per year = once = 1

t = time in years = 2010 to 2020 = 10 years

∴
`810 = p * (1+ (0.05)/(1)) ^(1*10)`

`810 = p * (1.05) ^(10)\\810= p(1.6289)` (dividing both sides by 1.6289)

p = 810 ÷ 1.6289 = 497.2 = 497 (to the nearest whole number)

∴ population in 2010 = 497