Answer:
a)
b) P(2) = 841 bacteria
c) P'(2) = 895 bacteria per hour
d) t = 4.3hr
Step-by-step explanation:
The equation of growth for the number of bacteria can be modeled by the following differential equation:
With solution.
In which P(t) is the population after t hours, P(0) is the initial population and r is the growth rate.
(a) Find an expression for the number of bacteria after t hours.
Initially 100 cells, so P(0) = 100.
After 1 hour, 290 cells, so P(1) = 290.
We apply this to the equation to find the value of r.
Applying ln to both sides of the equality.
So
(b) Find the number of bacteria after 2 hours.
This is P(2).
841 bacteria after 2 hours.
(c) Find the rate of growth after 2 hours.
(d) When will the population reach 10,000?
This is t when P(t) = 10,000. So
Applying ln to both sides