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?

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ishpiro's profile pic

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's profile pic

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.

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