SOLUTION: A GROUP OF SCIENTISTS STUDDIED THE EFFECT OF a chemical on various strands of bacteria. strain a started with 6000 cells and decreased at a constant rate of 2000 cells per hour aft

Question 1080293: A GROUP OF SCIENTISTS STUDDIED THE EFFECT OF a chemical on various strands 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 100 cells per hour after the chemical was applied. when will the strains have the same number of cells explain.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the general formula is:

f = p + r * x

f is the future value
p is the present value
r is the rate of change in the number of cells per hour.
x is the number of hours.

the first strain starts with 6000 cells and decreases at the rate of 2000 cells per hour.

the formula would be f = 6000 - 2000 * x

f is the future value
6000 is the present value
-2000 is the rate of change per hour.
x is then number of hours.

note that 6000 + (-2000 * x) is the sme as 6000 - 2000 * x

the second strain starts with 2000 cells and decreases at the rate of 100 cells per hour.

the formula would be f = 2000 - 100 * x

f is the future value
2000 is the present value
-100 is the rate of change per hour.
x is the number of hours.

note that 2000 + (-100 * x) is the same as 2000 = 100 * x

they will have the same number of cells when the future value of the first formula is equal to the future value of the second formula.

that happens when 6000 - 2000 * x is equal to 2000 - 100 * x

start with:
6000 - 2000 * x = 2000 - 100 * x
subtract 2000 from both sides of the equation and add 2000 * x to both sides of the equation to get:
6000 - 2000 = 2000 * x - 100 * x
simplify to get:
4000 = 1900 * x
divide both sides of the eqution by 1900 to get:
4000 / 1900 = x
solve for x to get x = 4000 / 1900 = 2.105263158 hours.

they will both have the same number of cells in 2.105263158 hours.

in the first formula, you get f = 6000 - 2000 * 2.105263158 = 1789.473684

in the second formula, you get f = 2000 - 100 * 2.105263158 = 1789.473684

they both have the same number of cells in 2.105263158 hours.

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