Question

A population declines by 0.6% each year. By what percentage does it decline each decade? (Round your answer to two decimal places.)

Answer 1

convert 0.6% into decimals.

Answer 2

0.006

now rounding this off,
0.01%

Answer 3

a decade is ten years. so wouldnt you just multiply .6 times 10?

Answer 4

The population after one year is:
\[P \times \frac{99.4}{100}\]The population after two years is:
\[P\times \frac{99.4}{100}\times\frac{99.4}{100}=P\times\left(\frac{99.4}{100}\right)^2\]The population after n years is:
\[P\times \left(\frac{99.4}{100}\right)^n\]

Answer 5

99.4 = 100-0.6 by the way, it's a simplification of \[P-P\times\frac{0.6}{100}\]

Answer 6

The reason you can't just multiply 0.6 by 10 is because 0.6% changes value each year. For example in year zero, say the population is 10000. 0.6% of this is 60, so the population is now 9940. The next year, the population drops by a further 0.6%, but wait! 100% is now 9940, so 0.6% must now equal something else as well (59.64 in fact). This happens year after year, with 0.6% representing a different number every year.