Question

This exercise uses the population growth model. The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. What was the initial size of the culture?

Answer 1

To find the initial size of the bacteria culture, we can use the formula for exponential growth. By plugging in the values given in the problem, we can solve for the initial size. The initial size of the culture is 100 bacteria.

Step-by-step explanation:

To find the initial size of the culture, we can use the formula for exponential growth:

N = N0 × (1+r)^t

Where:

• N is the final count of bacteria
• N0 is the initial count of bacteria
• r is the growth rate
• t is the time in hours

First, we'll plug in the values we have:

400 = N0 × (1+r)^2

25600 = N0 × (1+r)^6

Next, we can divide the second equation by the first equation to eliminate N0:

(1+r)^6 / (1+r)^2 = 25600/400

Simplifying the left side:

(1+r)^(6-2) = 64

Which simplifies to:

(1+r)^4 = 64

Now we can find the value of (1+r) by taking the fourth root of 64:

1+r = 2

r = 1

Finally, we can substitute the value of r back into one of the original equations to solve for N0:

400 = N0 × (1+1)^2

N0 = 400/4

N0 = 100