Strain A had 9000 cells and decreased at a rate of 3000 cells per hour. Strain B started with 4000 cells and decreased at a rate of 2000 cells per hour.

Question

When will the strains have the same number of​ cells? Give the ordered pair please!

Answer 1

Hi Sydney, the problem you posed can be translated directly into the following equation:

Let

t = number of hours

N_A(t) = number of cells in strain A after t hours = 9000 - 3000*t

N_B(t) = number of cells in strain B after t hours = 4000 - 2000*t

At first it would seem by solving N_A(t) = N_B(t), you should have your answer:

9000 - 3000*t = 4000 - 2000*t

-1000*t = -5000

t = 5

Plugging it back into the equation:

Left Hand Side: 9000 - 3000*5 = -6000

Right Hand Side: 4000 - 2000*5 = -6000

This is non-nonsensical result as both strains can't decrease to negative number of cells.

Applying some common sense to this problem, there is a lower bound on both functions and both strains should stop decreasing when number of cells reach 0.

For strain A, 9000 - 3000*t = 0 --> t = 3 hours

For strain B, 4000 - 2000*t = 0 --> t = 2 hours

So the sensible answer is that after 3 hours, both strains will have the same number of cells (0).

Answer 2

9000 - 3000h = 4000 - 2000h

5000 = 1000h

h = 5 hours

(5,-6000)

Well, if you copied the problem correctly, this is technically impossible, as after 5 hours, both strains would have -6000 cells after 5 hours, but if we're suspending reality for a math problem, your answer is above.