# Between 1980 and 1990, the population of deer in a national park increased by 40%. Between 1990 and 2000, the deer population increased by 20%. The deer population in 2000 was how many time greater...

Between 1980 and 1990, the population of deer in a national park increased by 40%. Between 1990 and 2000, the deer population increased by 20%. The deer population in 2000 was how many time greater than the deer population in 1980? I know the answer is 1.68 but I don't understand how to work it out. Can someone please explain it to me?

ishpiro | College Teacher | (Level 1) Educator

Posted on

Let's denote the population of deer in 1980 by x.

The population increase by 40% means that the population increased by 40% of x, or 0.4x. The population in 1990 is then x + 0.4x = 1.4x.

Between 1990 and 2000, the population increased by 20%. This is 20% of the population in 1990, which we found is 1.4x. 20% of 1.4x is 0.2(1.4x) = 0.28x.

The population in 2000 is then population in 1990 + 20% increase, which is

1.4x + 0.28x = 1.68x.

So, the population in 2000 is 1.68 times x, the population in 1980. This means the deer population in 2000 is 1.68 times greater than the deer population in 1980.

gsarora17 | (Level 2) Associate Educator

Posted on

Let the population of the deer in 1980 = x

Since the population of the deer increased by 40%

`:.`  Increase in population = (x*40)/100 = 0.4x

`:.`  Population of the deer in 1990 = x + 0.4x  = 1.4x

Now the population from 1990 to 2000 increased by 20%

`:.`  Increase in population = (1.4 x*20)/100 = 0.28x

Hence , Population of the deer in 2000 = 1.4 x + 0.28 x

= 1.68 x

Since the population of the deer in the year 1980 was assumed to be x , therefore the population in 2000 is 1.68 times of the population in 1980.

In other words we can say that population has increased by 68% from 1980 to 2000.