Answer:
a) The initial population is 125 bacteria.
b)
c) There are 1378 cells after 3 hours.
d) The rate of growth after 3 hours is of 1102 cells an hour.
e) The population will reach 200,000 in 9.22 hours.
Step-by-step explanation:
The population of this culture can be modeled by the following formula:
In which P(t) is the population after t hours, is the initial population, and r, as decimal, is the growth rate.
(a) Find the initial population.
Also
Replacing in this equation:
Applying ln to both sides
The initial population is:
The initial population is 125 bacteria.
(b) Find an expression for the population after t hours.
(c) Find the number of cells after 3 hours.
There are 1378 cells after 3 hours.
(d) Find the rate of growth after 3 hours.
This is P'(3).
So
The rate of growth after 3 hours is of 1102 cells an hour.
(e) When will the population reach 200,000?
Applying ln to both sides
The population will reach 200,000 in 9.22 hours.