Well, this problem is best solved by setting up a system of two linear equations.
A linear equation can be defined y=mx+b where b=initial value (when x=0), and m=rate of increase or decrease.
In the given example, the x-axis represents hour, and the y-axis, number of cells.
Chemical #1 initial value = b = 12000 cells rate = m = -4000 / hr The equation is therefore y1=-4000x+12000......................(1)
Similarly, for chemical #2 initial value = b = 6000 cells rate = m = -3000 / hr The equation is therefore y2=-3000x+6000 .......................(2)
The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when y1=y2 which means -4000x+12000 = -3000x+6000 transpose and solve for x 4000x-3000x = 12000-6000 1000x=6000 x=6 hours.
At 6 hours from the start, y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells
So the solution is x=6, y=-12000, or (6,-12000)
Physical interpretation Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero. Case 1: y=0 when x=3 Case 2: y=0 when x=2
Therefore, after three hours, both trials will have zero cells.
You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.