Question

A population of bacteria doubles every 15 hours. Initially, the population of bacteria is 40.

Answer 1

Answer:

The population of the bacteria after 40 hours is 254.

Step-by-step explanation:

The initial population is 40 and the population of bacteria doubles every 15 hours.

The population function is defined as

$P(t)=P_0\cdot (b)^{t}$

Where P₀ is initial population, b is exponential growth rate.

Since the population of bacteria doubles every 15 hours, therefore the growth rate is

$2^{\frac{1}{15}}$

$P(t)=40\cdot (2)^{\frac{1}{15}t}$

$P(t)=40\cdot (2)^{\frac{t}{15}}$

We have to find the population of the bacteria after 40 hours, so put $t=40$ in the above equation.

$P(t)=40\cdot (2)^{\frac{40}{15}}$

$P(t)=40\times 6.3496$

$P(t)=253.9842$

$P(t)\approx 254$

Therefore the population of the bacteria after 40 hours is 254.