Predict the population of bacteria for each situation and time period.
-55 bacteria that double every hour
a. after 3 hours b. after 5 hours
hmmm. what is
a. 55*2^3
b. 55*2^5
To predict the population of bacteria, we can use the formula:
P = P0 * (2^t)
Where:
P = population after a certain time period
P0 = initial population
t = time period
a. After 3 hours:
P0 = 55 (initial population)
t = 3 (time period)
P = 55 * (2^3)
P = 55 * 8
P = 440
So, after 3 hours, the population of bacteria would be 440.
b. After 5 hours:
P0 = 55 (initial population)
t = 5 (time period)
P = 55 * (2^5)
P = 55 * 32
P = 1760
So, after 5 hours, the population of bacteria would be 1760.
To predict the population of bacteria for each situation and time period, we need to understand how bacterial growth occurs.
For the given situation where there are 55 bacteria that double every hour, we can use the exponential growth formula:
P = P₀ * (2^(t/n))
where:
P = final population size
P₀ = initial population size
t = time period
n = time it takes for population to double
a. After 3 hours:
P₀ = 55 (initial population size)
t = 3 (time period)
n = 1 (since the bacteria double every hour)
Substituting the values into the formula:
P = 55 * (2^(3/1))
P = 55 * (2³)
P = 55 * 8
P = 440
So, after 3 hours, the population of bacteria is predicted to be 440.
b. After 5 hours:
P₀ = 55 (initial population size)
t = 5 (time period)
n = 1 (the bacteria double every hour)
Substituting the values into the formula:
P = 55 * (2^(5/1))
P = 55 * (2^5)
P = 55 * 32
P = 1760
So, after 5 hours, the population of bacteria is predicted to be 1760.