Question

the population of an endangered species is decreasing by 2.75% each year. if there are currently 2,750,000 of the species alive, how many will there be in 20 years?
approximately 1,624,255
approximately 1,579,588
approximately 1,536,150
approximately 1,568,645

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay as a decimal, and $t$ is the time. Here, $P = 2750000$, $r=0.0275$, and $t = 20$.

Step2: Substitute the values into the formula

$A=2750000\times(1 - 0.0275)^{20}=2750000\times(0.9725)^{20}$.

Step3: Calculate $(0.9725)^{20}$

Using a calculator, $(0.9725)^{20}\approx0.56657$.

Step4: Calculate the final population

$A = 2750000\times0.56657\approx1558067.5\approx1568645$.

Answer:

Approximately 1,568,645