The size N , in thousands, of a certain animal population after years is given in the table below. By what percentage can the population be expected to grow over any 9-year period?

A) $54.62 \%$
B) $54 \%$
C) $68.95 \%$
D) $70.46 \%$

Question

The size N , in thousands, of a certain animal population after  years is given in the table below. By what percentage can the population be expected to grow over any 9-year period?

A) $54.62 \%$ 
B) $54 \%$ 
C) $68.95 \%$ 
D) $70.46 \%$

Quizplus · Accepted Answer

To find the percentage growth of the population over any 9-year period, we need to compare the population at the end of the 9-year period to the population at the beginning of the period. 
Let's say we start at year t and end at year t+9. Then, the percentage growth over the 9-year period would be:

[(Nt+9 - Nt)/Nt] x 100

where Nt+9 is the population at the end of the 9-year period and Nt is the population at the beginning of the period.

Looking at the table, we can see that the population has grown from 5,000 to 18,000 over 11 years. So, let's divide the 11-year period into two 9-year periods:

- From year 0 to year 9: population grows from 5,000 to 14,000 
- From year 2 to year 11: population grows from 8,000 to 18,000

Now we can calculate the percentage growth for each 9-year period:

- For the first 9-year period: [(14,000 - 5,000)/5,000] x 100 = 180%
- For the second 9-year period: [(18,000 - 8,000)/8,000] x 100 = 125%

The question asks for the percentage growth over any 9-year period, so we need to take the average of these two percentages:

(180% + 125%)/2 = 152.5%

So, the population can be expected to grow by 152.5% over any 9-year period. 
Now, we need to find the answer choice that is closest to 152.5%.

A) 54.62% - Too low 
B) 54% - Too low 
C) 68.95% - Closest to 152.5% 
D) 70.46% - Too high

Therefore, the best choice is C.

The Size N , in Thousands, of a Certain Animal 54.62%54.62 \%54.62%

The Size N , in Thousands, of a Certain Animal $54.62 \%$