The size of a decreasing population is given by p(t)=P0(2)^-t/7 where p(t) represents the population as time, t, in years and p0 is the initial population what percent of the original population will be there after 10 years??
let the initial population be 1 or 100%
after 10 years:
pop= 1(2)^(-10/7)
= .3715
or 37.15%
To find the percent of the original population that will be present after 10 years, we need to calculate the value of p(10) and express it as a percentage of P0.
Given the population function p(t) = P0(2)^(-t/7), we substitute t = 10 into the equation to find p(10):
p(10) = P0(2)^(-10/7)
To convert this into a percentage, we need to calculate the fraction of the original population that remains after 10 years:
fraction = p(10) / P0 = (P0(2)^(-10/7)) / P0
Simplifying, we have:
fraction = (2)^(-10/7)
To convert this fraction into a percentage, we multiply it by 100:
percentage = fraction * 100 = (2)^(-10/7) * 100
Now, let's calculate the value:
percentage ≈ 49.366
Therefore, after 10 years, approximately 49.366% (or roughly 49.37%) of the original population will remain.