Abacteria culture grows with constant relative growth rate. after 2 hours there are 600 bacteria and after 8 hours the count is 75,000.
(a) find the initial population.
(b) find an expression for the population after t hours.
(c) find the number of cells after 3 hours.
(d) find the rate of growth after 3 hours.
(e) when will the population reach 200,000?

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.

78.59 is the mean

step-by-step explanation:

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743