Population growth math problem? thanks!?

Question

Hi! for some reason, word problems always give me problems.

here is the problem:

the population of Q in the year 1890 was 6250. Assume the population increased at a rate of 2.75% per year.

a) estimate the population in 1915 and 1940

b) approximately when did the population reach 50,000?

So if you could explain to me the steps to solving it, i would really appreciate it!

thank you!

Answer 1

Cool question.

First you have to set up an equation which gives you the population Q for the year Y.

I set this up by  starting with

Y - 1890

This means 1890 is like the year "zero"

Now we need the multiplier for a given year so we raise the adjusted year to the power of the percent they gave us, plus 1 to make it grow correctly:

(Y-1890)^1.0275

Finally we just multiply the year "zero" population by the multiplier to get our equation:

Q = 6250 x ( Y - 1890 ) ^ 1.0275

Now just plug in the numbers for step (a)

a) Q=6250*(1915-1890)^1.0275 = 170711

a) Q=6250*(1940-1890)^1.0275 = 347994

For step (b) we have to solve backwards:

50000=6250(Y-1890)^1.0275

(Y-1890)^1.0275=50000/6250

Y = (50000/6250)^(1/1.0275)+1890 = 1897.6 or between 1897 and 1898

Phew. That was really was hard. Is this a college class?