Question

A bacterial culture grows according to the formula P = P0 * a^t. If it takes 8 days for the culture to triple in size, how long will it take to double in size?

a) 4 days
b) 8 days
c) 12 days
d) 16 days

Answer 1

It will take approximately 4 days for the bacterial culture to double in size.

Step-by-step explanation:

To find out how long it will take for the bacterial culture to double in size, we need to determine the doubling time. In the formula P = P0 * a^t, the doubling time is the time it takes for the population to double, which can be represented as t. In this case, it took 8 days for the bacteria to triple in size. So, the doubling time can be calculated by solving the equation (P0 * a^8) = 3 * P0. Simplifying the equation, we have a^8 = 3. Taking the 8th root on both sides, we find that a = 1.173. Now, we can use the formula P = P0 * a^t and set P to be 2P0, since we want to find the time it takes for the population to double. Substituting the value of a, we have 2P0 = P0 * (1.173)^t. Simplifying the equation, we get (1.173)^t = 2. Taking the logarithm of both sides, we have t = log1.173(2), which is approximately 4.006. Therefore, it will take approximately 4 days for the bacterial culture to double in size.