The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Question

The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled. Find a5, he amount of water left in the tub after 5 minutes.

Answer 1

Hello, this is Mariam

a0 = 84

a1 = a0 - 12 = 84 - 12

a2 = a1 - 12 = 84 - 12 - 12

a3 = a2 - 12 = 84 - 12 - 12 - 12

a4 = a3 - 12 = 84 - 12 - 12 - 12 - 12

a5 = a4 - 12 = 84 - 12 - 12 - 12 - 12 - 12 = 84 - (5*12) = 24

with this formula, you can find an for every n, so for n = 7 you get a7 = 84 - (7*12) = 0 meaning that the gallon will be empty at the 7th minute.