Video Transcript
Ethan has 73 rabbits. He believes that he will have 𝑍
equal to 73 multiplied by 4.21 to the power of 𝑛 over three rabbits after 𝑛
months. How many rabbits does he expect to
have two months from now?
In this question, we are given an
expression for the number of rabbits that Ethan expects to have after 𝑛 months. It is 73 multiplied by 4.21 to the
power of 𝑛 over three, where 𝑛 is the number of months. We note that 73 is the number of
rabbits that Ethan started with. We need to work out the number of
rabbits he expects to have two months from now. This means we need to calculate the
number of rabbits 𝑍 when 𝑛 is equal to two. We have 𝑍 is equal to 73
multiplied by 4.21 to the power of two-thirds. Typing this into the calculator
gives us 190.3316 and so on.
Since the number of rabbits must be
an integer, we will round down. And we can therefore conclude that
two months from now, Ethan expects to have 190 rabbits. Note that we can use the equation
to calculate the expected number of rabbits at any point in the future; we
substitute the number of months from now for 𝑛.
