A group of scientists studied the effect of a chemical in various strains of bacteria. Strain A started with 6000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. Strain B started with 2000 cells and decreased at a constant rate of 1000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Write a system of equations and solve.
That was the exact word problem, word for word from the textbook.
Let's denote the time in hours as "t".
For Strain A:
The initial number of cells is 6000.
The rate of decrease is 2000 cells per hour.
So, the equation representing the number of cells for Strain A at any time "t" would be:
Number of cells for Strain A = 6000 - 2000t.
For Strain B:
The initial number of cells is 2000.
The rate of decrease is 1000 cells per hour.
So, the equation representing the number of cells for Strain B at any time "t" would be:
Number of cells for Strain B = 2000 - 1000t.
To find the time when both strains have the same number of cells, we can set the equations equal to each other and solve for "t":
6000 - 2000t = 2000 - 1000t
To solve for "t", we can simplify the equation:
4000 = 1000t
Divide both sides by 1000:
4 = t
Therefore, both strains will have the same number of cells after 4 hours.
To solve this problem, we need to set up a system of equations that represents the number of cells in each strain at a given time. Let's denote the number of hours since the chemical was applied as "t".
For Strain A, we know that it started with 6000 cells and decreased at a constant rate of 2000 cells per hour. So the equation for Strain A is:
A(t) = 6000 - 2000t
For Strain B, we know that it started with 2000 cells and decreased at a constant rate of 1000 cells per hour. So the equation for Strain B is:
B(t) = 2000 - 1000t
Now we need to find the time at which both strains have the same number of cells. This means we need to find a value of "t" for which A(t) = B(t). We can set up the equation:
6000 - 2000t = 2000 - 1000t
Now we can simply solve this equation to find the value of "t" when both strains have the same number of cells.
6000 - 2000t - 2000 + 1000t = 0
4000 - 1000t = 0
-1000t = -4000
t = -4000 / -1000
t = 4
Therefore, both strains will have the same number of cells after 4 hours.
no need for a system of equations. After x hours they will be the same if
6000-2000x = 2000-1000x
Unfortunately, strain B will be completely gone after 2 hours, right?
I suspect a typo or some missing information.