At the start of an experiment, there are 100 bacteria. If the bacteria follow an exponential growth pattern with a growth rate of 12%, what will be the population after 10 hours (round to the nearest bacteria)?
Spell check
if yu mean 12% per hour, then there will be
100*1.12^10
p=98
To find the population after 10 hours in an exponential growth pattern, we can use the formula:
P(t) = P0 * e^(rt)
Where:
P(t) is the population after time t
P0 is the initial population
e is the base of the natural logarithm (approximately 2.71828)
r is the growth rate (in decimal form)
t is the time period
In this case, the initial population (P0) is 100 bacteria, the growth rate (r) is 0.12 (12% expressed as a decimal), and the time period (t) is 10 hours.
First, let's calculate the exponential part of the formula:
e^(rt) = e^(0.12 * 10)
Using a calculator, we find that e^(1.2) is approximately 3.320116922.
Now, we can substitute this value into the formula:
P(t) = 100 * 3.320116922
Calculating this, we find that the population after 10 hours would be approximately 332 (rounded to the nearest whole number).