Question

Ethan is saving money in his piggy bank for his upcoming trip to Disney World. On the first day, he put in $12 and plans to add seven more dollars each day.

Part A: Write an explicit formula that can be used to find the amount of money saved on any given day.
Part B: How much money will he have on the 18th day?
Part C: The Disney trip is in 187 days from the day he started saving. How much money will he have on the 187th day?

Answer 1

Part A:
`S_(n) = 12 + 7(n - 1)`

Part B: $131

Part C: $1314

Explanation:

Ethan is saving money in his piggy bank for his upcoming trip to Disney World. On the first day, he put in $12 and plans to add seven more dollars each day.

Part A:

On the first day, he puts $12 in the piggy bank.

On the second day, he deposited $7 in it. So, after second day he has (12 + 7) = $19.

On the third day, he deposited $7 more in it. So, after third day he has (19 + 7) = $26.

In this way, the savings in the piggy bank are growing in an arithmetic sequence with first term $12 and a common difference $7.

Therefore, the explicit formula that can be used to find the amount of money saved on any given day is given by

`S_(n) = 12 + 7(n - 1)`

Part B:

Putting n = 18, we get the money that he will have on the 18th day, is given by
`S_(18) = 12 + (18 - 1) 7 = 131` dollars.

Part C:

The Disney trip is in 187 days from the day he started saving. Then he will have after 187 days
`S_(187) = 12 + (187 - 1)7 = 1314` dollars. (Answer)