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 3000 cells per hour after the chemical was applied. Strain B started with 4000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain.​

Answer 1

Strain A and Strain B will have the same number of cells after 8 hours when setting up the linear equations representing the decrease in cell count over time for each strain, and solving for the time it takes for these equations to intersect.

Step-by-step explanation:

To determine when the strains of bacteria will have the same number of cells, we can set up two linear equations that represent the number of cells over time for each strain and find the point where these equations intersect.

For Strain A, starting with 12,000 cells and decreasing at a rate of 3,000 cells per hour, the equation is:

A(t) = 12000 - 3000t

For Strain B, starting with 4,000 cells and decreasing at a rate of 2,000 cells per hour, the equation is:

B(t) = 4000 - 2000t

To find when they will have the same number of cells, we set A(t) equal to B(t):

12000 - 3000t = 4000 - 2000t

Simplifying the equation, we subtract 4000 from both sides and add 3000t to both sides:

8000 = 1000t

Then, we divide both sides by 1000 to find t:

t = 8 hours

Thus, after 8 hours, both strains will have the same number of cells.