Question

The concentration of bacteria B in millions per milliliter after x hours is given by B(x)=1.33e^0.15x. After how many hours will there be 31 million bacteria per milliliter?

Answer 1

21 hours

Explanation:

You want to find x such that B(x) = 31. Fill in the value and solve.

... 31 = 1.33e^(0.15x)

... 31/1.33 = e^(0.15x) . . . . divide by 1.33

... ln(31/1.33) = 0.15x . . . . take the natural log

... ln(31/1.33)/0.15 = x ≈ 20.992 . . . . hours

After 21 hours, the concentration will be 31 M/mL.