At the start of an experiment, there are 100 bacteria. If the bacteria follow an exponential growth pattern with a growth rate of 2%, what will be the population after 5 hours (round to the nearest bacteria)?
100 * 1.02^5
assuming you mean 2% per hour
if it is per minute it would be
100 * 1.02 ^300
To find the population after 5 hours, we can use the exponential growth formula:
P(t) = P0 * e^(rt)
Where:
P(t) is the population at time t
P0 is the initial population
e is the base of natural logarithms (approximately 2.71828)
r is the growth rate
t is time (in hours)
Given:
P0 = 100 (initial population)
r = 0.02 (growth rate)
t = 5 (time in hours)
Plugging in the values, we have:
P(5) = 100 * e^(0.02*5)
To calculate this, we need the value of e^(0.02*5), which is approximately 1.1047.
P(5) = 100 * 1.1047
Multiplying these numbers, we get:
P(5) ≈ 110.47
Rounding to the nearest whole number, the population after 5 hours is 110 bacteria.
To find the population after 5 hours, we can use the exponential growth formula:
N = N₀ * e^(r * t)
Where:
N₀ is the initial population
r is the growth rate as a decimal
t is the time period
In this case, the initial population (N₀) is 100 bacteria, the growth rate (r) is 2% or 0.02, and the time period (t) is 5 hours.
Now, let's plug in the values and calculate the population after 5 hours.
N = 100 * e^(0.02 * 5)
To evaluate this, we need to use the value of the mathematical constant 'e'. The value of 'e' is approximately 2.71828.
N = 100 * 2.71828^(0.02 * 5)
Now, let's calculate 0.02 * 5:
N = 100 * 2.71828^0.1
Using a calculator, raise the value of 'e' to the power of 0.1:
N ≈ 100 * 1.105170918
Finally, multiply 100 by 1.105170918 to get the population:
N ≈ 110.517
Since we rounded the initial population to the nearest whole number, we can also round the result to the nearest whole number:
N ≈ 111
Therefore, the population after 5 hours (rounded to the nearest bacteria) is approximately 111 bacteria.