Question

A population declines by 0.9% each year. By what percentage does it decline each decade? (Round your answer to two decimal places.)

Answer 1

it declines by .9% each year, which implies 99.1% of what was at the begginning of that year is left at the end of the year.

we can write 99.1% as a decimal equivalent of .991. So every year, the previous years population is multiplied by .991

which results in an exponential decay equation given by p(t) = Po(.991)^t

where t is in years,

p(t) is the population left after t years, and

Po is the initial value of population

.991 ^10 = .913558, or 91.35588% of the original population is left after one decade, stating the population declines by 8.64411% each decade

so answer is 8.64%