Video: Evaluating Exponential Equations Involving Exponential Growth

Karim has 73 rabbits. He believes he will have 𝑍 = 73(4.23)^(𝑛/3) rabbits after 𝑛 months. How many rabbits does he expect to have 2 months from now?

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Video Transcript

Karim has 73 rabbits. He believes he will have 𝑍 equals 73 multiplied by 4.23 to the power of 𝑛 divided by three rabbits after 𝑛 months. How many rabbits does he expect to have two months from now?

If we look at the equation, 73 multiplied by 4.23 to the power of 𝑛 divided by three, we need to replace 𝑛 with the number of months.

In this case, as we’re trying to work out how many rabbits he expects to have in two months, 𝑛 will be equal to two.

This means that we need to calculate 73 multiplied by 4.23 to the power of two-thirds. Typing this into the calculator gives us a value for 𝑍, the number of rabbits, of 190.933.

As we can only have a whole number of rabbits, we can say that Karim expects to have 191 rabbits two months from now.

We could use this equation or formula to calculate the number of rabbits anytime in the future by replacing 𝑛 with the number of months.

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