Problem of the Week - Algebra and Up - April 4, 2021 to April 10, 2021

Algebra and Up: 

Question: The siberian unicorn, a ginormous prehistoric rhinoceros-like animal, survived until around 37,000 BCE. Assume the population of Siberian unicorns was exactly 262,144 in the year 39,000 BCE and followed the model 

f(t) = 262,144(2)^-t, a function of t time in centuries. According to the model, what year did the population of Siberian unicorns decline to exactly 1? You may use your calculator to solve this problem.

Answer: 37,200 BCE

Solution: One way to solve this problem is to notice that since 262,144 is being multiplied by 2 raised to a negative power, the population will halve itself each century. We can find out how many centuries by finding what power we raise 2 to in order to get 262,144. Since 2¹⁸ = 262,144, it takes 18 centuries for the population to fall from 262,144 to 1, making the year 39,000 – 1,800 = 37,200 BCE.