Question 702020
The bacteria in a certain culture double every 7.1 hours. The culture has 6,500 bacteria at the start. How many bacteria will the culture contain after 4 hours?
.
General exponential growth/decay equation:
A = Pe^(rt)
where
A is amount after time t
P is initial amount
r is growth/decay rate
t is time
.
From: "The bacteria in a certain culture double every 7.1 hours." we can determine r:
P/2 = Pe^(r*7.1)
1/2 = e^(r*7.1)
.5 = e^(r*7.1)
ln(.5) = r*7.1
ln(.5)/7.1 = r
-0.09763 = r
.
Now, we can answer:
How many bacteria will the culture contain after 4 hours?
A = Pe^(rt)
A = 6500e^(-0.09763*4)
A = 6500e^(-0.3905055)
A = 4398.65 (answer)