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 6-year period?

A) $36.97 \%$
B) $36 \%$
C) $41.85 \%$
D) $41.87 \%$

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 6-year period?

A) $36.97 \%$ 
B) $36 \%$ 
C) $41.85 \%$ 
D) $41.87 \%$

Quizplus · Accepted Answer

To calculate the percentage growth over a 6-year period, we need to use the formula:

Percentage growth = [(final population/initial population)^(1/6) - 1] x 100%

Using the data from the table, we can calculate the percentage growth for each 6-year period as follows:

- From year 1 to year 6: Percentage growth = [(64/36)^(1/6) - 1] x 100% = 10.93%
- From year 2 to year 7: Percentage growth = [(148/64)^(1/6) - 1] x 100% = 18.16%
- From year 3 to year 8: Percentage growth = [(288/148)^(1/6) - 1] x 100% = 14.91%
- From year 4 to year 9: Percentage growth = [(412/288)^(1/6) - 1] x 100% = 11.47%
- From year 5 to year 10: Percentage growth = [(500/412)^(1/6) - 1] x 100% = 6.94%
- From year 6 to year 11: Percentage growth = [(540/500)^(1/6) - 1] x 100% = 2.67%

To find the overall percentage growth over any 6-year period, we can take the average of these values:

Average percentage growth = (10.93% + 18.16% + 14.91% + 11.47% + 6.94% + 2.67%)/6 = 11.95%

Therefore, the population can be expected to grow by approximately 41.85% over any 6-year period (100% + 11.95% = 111.95%) which is Choice C.

The Size N , in Thousands, of a Certain Animal 36.97%36.97 \%36.97%

The Size N , in Thousands, of a Certain Animal $36.97 \%$