How to figure out the town's population

Question

A town’s population is increasing at a constant rate. In 2015 the population was 55,000. By 2021 the population is 86,000. If this linear trend continues, predict the population in 2025.

Answer 1

2015 55,000

2021 86,000

(86-55)/(21-15) = 31/6 = (P-55)/(y-15)

31y-31(15) = 6P-6(55)

31(25)-31(15) = 6(P-55)

P -55 = 31(10)/6

P = 55+ 310/6 = 55+51.666..

Population in 2025 is 106,666,667

= 106 2/3 million

in 6 years, 2015 to 2021 it increased 31 million

that's 31/6= 5 1/6 million per year

in 2021 it's 86 million

in 2025, 4 years later, it's 86+20 2/3 = 106 2/3 million

UNLESS by constant rate of increase, you meant a natural exponential growth rate, then

A=Pe^rt where r=a constant percentage annual rate of increase

86=55e^6r

ln(86/55) =6r

r = ln(86/55)/6 = about 7.45% yearly rate of increase

P =55e^10(.0745) = 55e^.745 = about 115.85 million

when you say "linear" you likely want the 1st solution: 106 2/3 million in 2025. Although an exponential growth rate is more realistic for population increases. still both predictions for 2025 population are within 10% of each other, a typical margin of error. A "linear" annual increase means a decreasing percentage increase. A "constant" percentage rate of increase means an exponential growth rate. It's all basically the same distinction in finance between continuous compounding and simple interest.