Question

I don't really understand what I have to do here,Please help:) I don't want the answer
In 1820 the population of a midwest city was 19,000. By 1830 it had grown to 22,000. If it continues to grow at the same rate, what will the population be in 1856? Give your answer to the nearest whole number.

Answer 1

The growth rate is (3,000/19,000) or 0.15789473 every 10 years.
So, every 10 years the population increases by 1.15789473
So, in 1830 it is 19000*1.15789473 or 22,000
Population = 19,000 * (1.15789473)^n where 'n' is the number of decades since 1820
Population 1840 = 19000 * (1.15789473)^2 = 25,474
We have to find the 1856 population which is 3.6 decades since 1820.
Population 1856 = 19000 * (1.15789473)^3.6 = 32,208

See? It's just that simple - LOL

Answer 2

Assume it grows by the same number of people per year.
Get that number by taking (22,000-19,000)/(10 years) = 300/year
add that number 26 times to go from 1830 to 1856.

popn becomes 22000+26*300= 29800

However, "nearest whole number" suggests simple additive model not good enough.

Try constant percentage growth at annual rate r, so that each year
is (1+r) times the previous year. Like compound interest.

Then have 22000= 19000( 1+r)^10

1 + r is 10th root of (22/19)
1 + r + (22/19)^0.1 = 1.0148

use this for compound growth for 26 years from 1830

popn in 1856 = (22000)(1.0148)^26 = (22000)(1.464) =32208

Note this is substantially larger than the additive model.

Answer 3

douglaswinslowcooper
It's good to see we both came up with the correct answer.

Answer 4

@wolf1728 , @douglaswinslowcooper Thank you:)