When you add 100 years, you have to triple the population each time. Let's find out how many centuries were needed first.

100000 * 3^n = 72900000

How did I get this formula? Simple :

After 1 century: 100,000 * 3
After 2 centuries: 100,000 * 3 * 3 = 100,000 * 3^2
After 3 centuries: 100,000 * 3^2 * 3 = 100,00 * 3^3
.....
So After n centuries: 100,000 * 3^n


=> 3^n = 729 = 3 * 243 = 3 * 3^5 = 3^6

=> n = 6

So it took 6 centuries from the year 1200 to reach 72,900,000

So it was the year 1800 when this population was reached.

rakeshmeher wrote:A nation's population triples every 100 years. If the population was 100,000 in the year 1200, in what year was the population 72,900,000?

Any short method !!!!!!!!!!!!!!

When an amount keeps being multiplied by the same value over and over, use the formula for exponential change:

Final Amount = Original Amount * Multiplier^(number of changes)

In the problem above:

The final amount is 72,900,000
The original amount is 100,000
The multiplier is 3 (because the population keeps tripling)

What we don't know is the number of changes: the number of times the population will have to triple in order to reach 72,900,000. We need to solve for this value.

So plugging our known values into the formula, we get:

72,900,000 = 100,000 * 3^x
729 = 3^x
Since 3^6 = 729, x = 6.

The population has to triple 6 times. Since it triples every 100 years, 6 * 100 = 600 years will be needed for the population to reach 72,900,000.

Since the starting year is 1200, 1200+600= 1800.

1200+100*n=100000*3^n

100000*3^n=72900000

3^n=729

n=6

1200+100(6)=1800

A nation's population triples every 100 years. If the population was 100,000 in the year 1200, in what year was the population 72,900,000?

The change of population from 100,000 to 72,900,000 can also be written as from 1 to 729 ( for simplification, divide both numbers by 100,000.

729 = 3^6 and 1 = 3^0.

So the change from 1 - 1(3) { or 3^0 - 3 ^1) takes 100 yrs. So the sequence is

3^0 3^1 3^2 3^3 3^4 3^5 3^6
6 spaces with each signifying 100 yrs sums to 600 yrs.