Question

A town has a population of 100,000. The population increases in a geometric sequence by 3% (0.03) each year. What is the population in 15 years?

Answer 1

Formula

r=t1/tn-1

tn=t1r^n-1

Answer 2

1 year later, population = 100,000 + 0.03*100,000 = 100,000*(1 + 0.03)
2 years later,
population = (100,000*(1+ 0.03)) + 0,03*(100,000*(1 + 0.03))
= 100,000*(1 + 0,03)*(1 + 0,03) = 100,000*(1+0,03)^2
and so on
so, the formula of the population for n years later = 100,000*(1 + 0.03)^n
15 years later, substitute n = 15, and you'll get the answer

Answer 3

So 100,000(1 + 0.03)^15

Answer 4

155797. @alicealc

Answer 5

yes