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.

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation:

the circumference of a circle is, 10.676 cm.

step-by-step explanation:

the formula for circumference of a circle is given by:

where

c is the circumference of a circle and

d is the diameter of a circle.

given: diameter(d) = 3.4 cm and use

substitute these values in [1] we get;

cm

therefore, the circumference of a circle is, 10.676 cm