Bacteria growth. A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 h there are 10,000 bacteria. At the end of 5 h there are 40,000 bacteria. How many bacteria were present initially

1250 bacteria

Step-by-step explanation:

The formula for Exponential Growth is given as:

P(t)= Poe^rt

Where

P(t) = Population after time t

Po = Initial Population

r = growth rate

t = time

Hence, solving for the above question , we have to find Po

Making Po the subject of the formula

Po = P(t)/e^rt

Step 1

Find the Exponential growth rate

At the end of 3 h there are 10,000 bacteria.

Hence:

Po = 10000/e^3r Equation 1

At the end of 5 h there are 40,000 bacteria.

Po = 40000/e^5r Equation 2

Equating both equations together,

10000/e^3r = 40000/e^5r

Hence:

e^5r/e^3r = 40000/10000

e^2r = 4

Take the In of both sides

In (e^2r) =In 4

2r= In 4

r = In 4/2

r = In 2

Step 2

Solve for Po(Initial Population)

Using Equation 2

Po = 40000/e^5r Equation 2

r = In2

Po = 40000/e^5 × In 2

Po = 40000/2⁵

Po = 1250 bacteria.

Therefore, they was 1250 bacteria initially