Question

The rate at which ice in a skating pond is melting is given by dV/ft = -4t - 2
Where V is volume of the ice in cubic inches and t is time in days after March 1st. Skaters can use the pond as long as the volume is greater than 3 cubic ft. If the ice is 5cubic ft in march 1st, when is the last day it will be safe on the pond?

Answer 1

if dV/ft = -4t - 2
V = -2t^2 - 2t + c
if March 1 ---> t = 0 , and when t=0 , V = 5
5 = 0-0 + c
V = -2t^2 - 2t + 5
so we want to know when V = 3
3 = -2t^2 - 2t + 5
2t^2 + 2t - 2 = 0
t^2 + t - 1 = 0
t = (-1 ± √5)/2 = .618 or a negative

Bad news, the pond is only safe on March 1

check:
when t = 1 ---> March 2nd
V = -2 - 2 + 5 = 1 cubic foot, not safe