A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000. a. Find the initial population b. Find an expression for the population after t hours.

So, the initial population of the bacteria culture is 80.003 and the expression after t hours is P(t)=80.003 e^(0.8047\times t).

Step-by-step explanation:

Given:

A bacteria culture with constant relative rate.

No. of bacteria =        Time () = hrs

No.of bacteria =    Time () = 8 hrs

Here the growth is exponential.

Formula to be used.

                                        = Initial population

According to the question.

                ...equation (i)

           ...equation (ii)

Dividing equation (ii) with (i)

⇒

⇒

⇒

Now using function both sides.

⇒

⇒  using rule

⇒

And from logarithmic rule

⇒

⇒

Now plugging this k value in any of the equation we can find the initial population.

a)

Then,

The initial population of the bacteria culture is 80.003

b)

Expression for the population after hours.

So, the initial population of the bacteria culture is 80.003 and the expression after t hours is P(t)=80.003 e^(0.8047\times t).

right

step-by-step explanation:

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: