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
Hint:
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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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