Let y be the number of cells, in thousands, and t the time in hours. In Strain A there were initially 6 thousand cells and each hour the number decreased by 2 thousand cells. Let's write an equation that describes the situation.
y=6-2 t
In Strain B we started with 2 thousand cells and the rate of decrease is 1 thousand cells per hour. We can also write this as an equation.
y=2-1 t
By combining the equations we get a system of equations.
y=6-2 t y=2-1 t
Let's solve this system graphically. We limit the domain to t≥ 0 since that is when the study started.
As we can see, the graphs intersect at (4,- 2). This is counter-intuitive as the graphs describe the number of bacteria and that cannot be less than 0. Therefore, we have to limit our range to y≥ 0.
When we limit the range to non-negative values the system of equations has no solutions.
However...
The strains do have the same number of cells when they are both 0 — after all, the bacteria have died. Let's view this graphically.
When all the cells in Strain A have died, y=0, both strains have the same number of cells. Let's find when this happens.
