When will the strains have the same number of cells?

Question

A group of scientists studied the effect of a chemical on various strains
of bacteria. Strain A started with 12000 cells and decreased at a constant rate of
4000 cells per hour after the chemical was applied. Strain B started with 60006000 cells
and decreased at a constant rate of 3000 cells per hour after the chemical was
applied. When will the strains have the same number of? cells? Explain

Answer 1

I cannot help wondering if there is a misprint involved here.

 

Strain A starts at 12000 cells and decreases at 4000/hr until the population is eliminated in 3 hrs.

 

Strain B starts at 60006000 and decreases at a rate of 3000/hr.  After three hours the population of Strain B is 59997000.  It won't equal the population of Strain A until it, too, has a population of zero, which won't occur until 20002 hours after the application of the chemical.

 

(If Strain B starts with a population of 6000 and decreases at a rate of 3000/hr, its population will reach zero after two hours.  Strain A, as we saw earlier, won't reach zero population until the third hour.)

 

Either way the solution to the problem is tied to the lower bound of the two populations.  One reaches zero first, then the other catches up.