Question

What is the explicit definition for the sequence that represents the potatoes left in the bucket after n minutes, given that Hal removes and cleans 4 potatoes per minute from a bucket initially holding 10 potatoes?

a) Pₙ = 10 - 4n
b) Pₙ = 4n - 10
c) Pₙ = 10 - n
d) Pₙ = 4n + 10

Answer 1

The explicit definition for the sequence of potatoes left after n minutes is Pₙ = 10 - 4n, as this subtracts the number of potatoes cleaned (4 for each minute that passes) from the initial amount.

Step-by-step explanation:

The explicit definition for the sequence that represents the potatoes left in the bucket after n minutes, given that Hal removes and cleans 4 potatoes per minute from a bucket initially holding 10 potatoes is Pn = 10 - 4n. This formula is derived by taking the initial amount of potatoes and subtracting the number Hal cleans per minute, multiplied by n, the number of minutes that have passed. For every minute that goes by, 4 potatoes are being removed. So, after n minutes, 4n potatoes will have been removed from the original 10.