Question 1080293
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.