Respuesta :
Since strain A started with 12,000 cells and decreased at a constant rate of 3000 cells per hour, we get that the cell population of strain A after t hours is:
[tex]12000-3000t\text{.}[/tex]Since strain B started with 4000 cells and decreased at a constant rate of 2000 cells per hour, we get that the cell population of strain B after t hours is:
[tex]4000-2000t\text{.}[/tex]If strain A and strain B have the same number of cells, then we can set the following equation:
[tex]12000-3000t=4000-2000t\text{.}[/tex]Subtracting 4000 from the above equation we get:
[tex]8000-3000t=-2000t\text{.}[/tex]Adding 3000t to the above equation we get:
[tex]8000=1000t\text{.}[/tex]Dividing by 1000 we get:
[tex]t=8.[/tex]Now, notice that, substituting t=8 in the first expression in the answering tab we get:
[tex]12000-8\cdot3000=12000-24000=-12000.[/tex]But we cannot get a negative number of cells, therefore this solution has no real meaning in the context of the problem.
Now, notice that substituting t=2 in the second expression we get:
[tex]4000-2000\cdot2=4000-4000=0.[/tex]Therefore after 2 hours, strain A has 0 cells, and this number does not change with time (because we cannot get a negative number of cells).
Now, notice that substituting t=4 in the expression we get that:
[tex]12000-3000\cdot4=12000-12000=0.[/tex]Therefore after 4 hours, strain B has 0 cells.
Then, after 4 hours after the chemical was applied both strains will have 0 cells.
Answer: 4 hours after the chemical was applied.
