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Fill in the tableWrite an explicit and recurisive equationHow many days will it take for the candy to be gone?

Fill in the tableWrite an explicit and recurisive equationHow many days will it take-example-1
User Loisann
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1 Answer

12 votes
12 votes

Since each day, the amount of candy that Augustus will give away is 60% of the actual amount of candy, the amount of candy that has on day n depends on the amount of candy remaining from the day n-1. Let C_n be the amount of candy remaining on day n.

Since 60% of the candy from the day n-1 will be given away, then only 40% from the candy of the day n-1 will remain on day n. Then:


\begin{gathered} C_n=(40)/(100)* C_(n-1) \\ =0.4C_(n-1) \end{gathered}

Since the amount of candy on day 1 is 100,000, then the recursive formula is:


\begin{gathered} C_n=0.4C_(n-1) \\ C_1=100,000 \end{gathered}

After n-1 days, the initial amount of candies gets multiplied by a factor of 0.4 n-1 times. Then, the explicit formula for the amount of candies that remain on day n (after n-1 days) is:


\begin{gathered} C_n=(0.4)^(n-1)* C_1 \\ =0.4^(n-1)*100,000 \end{gathered}

Therefore, the answers are:

Explicit formula:


C_n=0.4^(n-1)*100,000

Recursive formula:


\begin{gathered} C_n=0.4* C^{}_(n-1) \\ C_1=100,000 \end{gathered}

User Pchajer
by
3.0k points
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