Question

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 8000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. Strain B started with 3000 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? Explain.

Answer 1

We have the following:

We must calculate the equation that represents each strain

$\begin{gathered} \text{Strain A} \\ A=8000-2000h \\ \text{Strain B} \\ B=3000-1000h \end{gathered}$

where h is the number of hours

We equalize the equations and we can calculate the number of hours when they will be equal and thus you can calculate the number of cells that there would be

$\begin{gathered} 8000-2000h=3000-1000h \\ 2000h-1000h=8000-3000 \\ h=\frac{5000}{1000} \\ h=5 \end{gathered}$

we calculate the number of cells

$\begin{gathered} A=8000-2000\cdot5=-2000 \\ B=3000-1000\cdot5=-2000 \end{gathered}$

The ordered pair is:

$5,-2000$