A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 9000 cells and decreased at a constant rate of 3000 cells per hour after the chemical was applied. Strain B started with 4000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain

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25-01-2017
Mathematics

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A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 9000 cells and decreased at a constant rate of 3000 cells per hour after the chemical was applied. Strain B started with 4000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain

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LammettHash LammettHash · Answer 1 · 2017-01-25T16:37:26-05:00

The number of cells of strain A follow the linear model \(C_A=9000-3000t\), where \(C_A\) denotes the number of cells of that strain and \(t\) is time in hours. Meanwhile, strain B follows \(C_B=4000-2000t\). The time \(t\) when both strains have the same number of cells is the intersection of these two lines, or the solution to

\(9000-3000t=4000-2000t\)

You have

\(5000=1000t\implies t=5\)

so after 5 hours, both strains should have the same number of cells.