Question Video: Evaluating Exponential Equations Involving Exponential Growth | Nagwa Question Video: Evaluating Exponential Equations Involving Exponential Growth | Nagwa

Question Video: Evaluating Exponential Equations Involving Exponential Growth Mathematics • Second Year of Secondary School

Ethan has 73 rabbits. He believes that he will have 𝑍 = 73(4.21)^(𝑛/3) rabbits after 𝑛 months. How many rabbits does he expect to have 2 months from now?

01:49

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.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy