Answer:
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
