Answer:
The initial bacteria population is 238
Step-by-step explanation:
Let us have the increase as an exponential equation
P(t) = I(1 + r)^t
where P(t) is the count at a particular time
r is the percentage increase
I is the initial population
t is the time
So for 5 minutes, we have
348 = I(1 + r)^5
For 20 minutes
1088 = I(1 + r)^20
Divide the second equation by the first
1088/348 = I(1 + r)^20/I(1 + r)^5
3.13 = (1 + r)^15
Take the ln of both sides
ln 3.13 = 15 ln (1 + r)
ln 3.13/15 = ln (1 + r)
0.0761 = ln (1 + r)
1 + r = e^0.0761
1 + r = 1.079
r = 1.079-1
r = 0.079 which is 7.9%
So per minute. we have an increase of 7.9%
So let’s get I by substituting
From;
348 = I(1 + 0.079)^5
348/1.079^5 = I
I = 237.9 which is 238 to the nearest whole number
