The amount of water left in the tub after 5 minutes is; 24 gallons
How to solve recursive formula?
The given recursive formula is expressed as;
aₙ = aₙ ₋ ₁ - 12
We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.
Thus, when n = 1, we have;
a₁ = a₁ ₋ ₁ - 12
a₁ = a₀ - 12
a₁ = 84 - 12
a₁ = 72
Then;
a₂ = a₁ - 12
a₂ = 72 - 12
a₂ = 60
It will seem that it follows a sequence pattern of;
aₙ = 84 - 12n
Thus;
a₅ = 84 - 12(5)
a₅ = 24 gallons
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