Question

in 2010 Small Town’s population was 1,759 people. If it’s declining by 2% each year, what would be the population in 2020? how long till the population is less than 1,000?

Answer 1

If the population decreases by 2% each year, that can be represented by multiplying the population by 0.98 mathematically. So if it decreases by 2% each year, an equation we can use is:

P*(0.98)^t,
where P is the current population and t is the number of years.

So in 2020, that would be 10 years from now, so the population would be:

1759*(0.98)^10 = 1437.23
Or about 1437 people.

How long till it is less than 1000? We can set up an inequality and solve:

1759*(0.98)^t < 1000

(0.98)^t < 1000/1759
t*ln(0.98) < ln(1000/1759)
t > ln(1000/1759)/(ln(0.98)) (swap the sign because ln(0.98) is a negative #)
t > 27.95

So the population would be below 1000 in about 28 years, or 2038.