Question #74e81

1 Answer
Dec 14, 2017

3252 bacteria

Explanation:

At the start, t=0, the initial number of bacteria (N_0) is 2000. After 6 hours (t=6), the number of bacteria (N) is now 2400.

Therefore, at t=6, the following exponential equation can be formed (with some constant k).

2400 = 2000*e^(6k)

Divide both sides by 2000:

1.2 = e^(6k)

Take the logs of both sides:

ln(1.2) = ln(e^(6k))

Since ln(e^x) = x, this can be rephrased as:

ln(1.2) = 6k

k = ln(1.2)/6 = 0.03038692613

Going back to the original equation, we can find the number of bacteria at t=16:

N = 2000 * e^(0.03038692613 * 16) = 3252