MATH SOLVE

5 months ago

Q:
# plz help with this word problem

Accepted Solution

A:

Well, this problem is best solved by setting up a system of two linear equations.

A linear equation can be defined

y=mx+b

where

b=initial value (when x=0), and

m=rate of increase or decrease.

In the given example, the x-axis represents hour, and the y-axis, number of cells.

Chemical #1

initial value = b = 12000 cells

rate = m = -4000 / hr

The equation is therefore

y1=-4000x+12000......................(1)

Similarly, for chemical #2

initial value = b = 6000 cells

rate = m = -3000 / hr

The equation is therefore

y2=-3000x+6000 .......................(2)

The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when y1=y2

which means

-4000x+12000 = -3000x+6000

transpose and solve for x

4000x-3000x = 12000-6000

1000x=6000

x=6 hours.

At 6 hours from the start,

y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells

So the solution is x=6, y=-12000, or (6,-12000)

Physical interpretation

Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero.

Case 1: y=0 when x=3

Case 2: y=0 when x=2

Therefore, after three hours, both trials will have zero cells.

You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.

A linear equation can be defined

y=mx+b

where

b=initial value (when x=0), and

m=rate of increase or decrease.

In the given example, the x-axis represents hour, and the y-axis, number of cells.

Chemical #1

initial value = b = 12000 cells

rate = m = -4000 / hr

The equation is therefore

y1=-4000x+12000......................(1)

Similarly, for chemical #2

initial value = b = 6000 cells

rate = m = -3000 / hr

The equation is therefore

y2=-3000x+6000 .......................(2)

The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when y1=y2

which means

-4000x+12000 = -3000x+6000

transpose and solve for x

4000x-3000x = 12000-6000

1000x=6000

x=6 hours.

At 6 hours from the start,

y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells

So the solution is x=6, y=-12000, or (6,-12000)

Physical interpretation

Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero.

Case 1: y=0 when x=3

Case 2: y=0 when x=2

Therefore, after three hours, both trials will have zero cells.

You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.