Question

In 1962, the population of a bird species was 2,000. The population *k *years after 1962 were 48, and *k *satisfies the equation above. Which of the following is the best interpretation of the number 61 in this

context?

- The population
*k *years after 1962 - The value of
*k *when the population was 48 - The difference between the population in 1962 and the population
*k *years after 1962 - The average decrease in the population per year from 1962 to
*k *years after 1962

*k*years after 1962*k*when the population was 48*k*years after 1962*k*years after 1962Hint:

**Hint:**

We need to understand every term in the equation given. We are given the number of bird species in a year 1962 and the number of

birds after *k* years. So, we are given that the relation between the years passed and the number of birds species satisfy the equation.

## The correct answer is: The average decrease in the population per year from 1962 to *k *years after 1962

### The given equation is

Given,

Number of bird species in year 1962 = 2000

Number of bird species in year 1962+*k *= 48

Solving the above equation for *k*, we get;

Also, *k* satisfies the above equation.

Thus, the population of the bird species in the year (1962+32=)1994 is given by 48.

Rearranging the equation , we get

Clearly, the right hand side of the above equation gives the average decrease in population from 2000 to 48, in k=32 years.

In other words,

61 denotes the average decrease in population per year from 1962 to k years after 1962.

The correct option is D)

.

**Note:**

This question could also be solved by eliminating the options. Option A is wrong as the population *k* years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population *k *years after 1962 is given by 2000-48=1952.

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In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

**Note: **

As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x