Originally, a Petri dish contained 200,000 bacteria. After a scientist applied an antibiotic, the number of bacteria decreased by 75% per hour.
Which function could model this situation?
How many bacteria will be in the Petri dish after 3 hours?
Round your answer to the nearest whole number.
The function that could model this situation is a exponential decay function, since the number of bacteria is decreasing by a certain percentage each hour.
We can use the formula for exponential decay:
N(t) = N₀ * e^(rt)
Where:
N(t) = the number of bacteria at time t
N₀ = the initial number of bacteria
r = the decay rate (as a decimal)
t = time in hours
In this case, N₀ = 200,000 and the decay rate is 75% or 0.75. Since the number of bacteria is decreasing, the decay rate r will be negative.
Substituting the known values into the formula:
N(t) = 200,000 * e^(-0.75t)
Now we can find the number of bacteria in the Petri dish after 3 hours by substituting t = 3 into the equation:
N(3) = 200,000 * e^(-0.75(3))
N(3) ≈ 200,000 * e^(-2.25)
N(3) ≈ 200,000 * 0.1054
N(3) ≈ 21,080
Therefore, there will be approximately 21,080 bacteria in the Petri dish after 3 hours.