In this lesson, we will learn how to solve real-world problems involving exponential decay, which can be modeled by the function f(t) = ae⁻ᵏᵗ, such as half-life problems.

Q1:

Hannah and Mason are playing a game where they roll 6-sided dice, and then they remove all the dice showing a 1. Then they roll the remaining dice and remove all the dice showing a 1 again, and so on.

Hannah and Mason started with 42 dice. According to the law of probability, find an explicit formula for the number of dice remaining after 𝑟 rounds of the game.

How many rounds does it take to remove roughly 2 3 of the dice?

Q2:

Two cars are bought at the same time. One of them costs $ 2 7 0 0 0 and depreciates at 7 % each year. If the second car costs $ 3 9 0 0 0 , at what rate does it depreciate if they have the same value after 5 years? Give your answer to one decimal place.

Q3:

Two vehicles are bought in the same year. One car costs $27 000 and depreciates at a rate of 6 % per year. The second car is more expensive but depreciates faster, at 1 0 % per year. How much must this car cost if the two have exactly the same value after 4 years? Give your answer to the nearest dollar.

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