Question

a bacteria culture initially contains 2500 bacteria and doubles every half hour.

find the size of the bacterial population after 100 minutes.

find the size of the bacterial population after 10 hours.

Explanation:

Step1: Define the growth model

$$P(t) = P_0 \cdot 2^{\frac{t}{d}}$$

Step2: Identify the given parameters

$$P_0 = 2500, \quad d = 30 \text{ minutes}$$

Step3: Calculate population after 100 minutes

$$P(100) = 2500 \cdot 2^{\frac{100}{30}} \approx 25198.42$$

Step4: Convert 10 hours to minutes

$$t = 10 \times 60 = 600 \text{ minutes}$$

Step5: Calculate population after 10 hours

$$P(600) = 2500 \cdot 2^{\frac{600}{30}} = 2500 \cdot 2^{20} = 2621440000$$

Answer:

The size of the bacterial population after 100 minutes is approximately 25198.
The size of the bacterial population after 10 hours is 2621440000.