Question

In a petri dish, a certain type of bacterium doubles in number every 40 minutes. There were originally 64, or 2, bacteria in the dish. After 120 minutes, the number of bacteria has doubled 3 times, multiplying by 2^3. Now the population of bacteria is 2^6. Expressed as a power, how many bacteria are in the petri dish after 120 minutes?

A. 2^18
B. 2^9
C. 2^49
D. 2^23

Answer 1

After 120 minutes, the number of bacteria in the petri dish, which originally contained 26 or 64 bacteria, will have doubled three times, leading to a resulting population represented by the power 29.

Step-by-step explanation:

The number of bacteria in the petri dish after 120 minutes, expressed as a power, is 29.

To determine the final population of bacteria, we know that the bacteria double in number every 40 minutes. Starting with 26 bacteria, after 120 minutes, which is three 40-minute intervals, the bacteria would have doubled three times. That is, they multiply by 23. So, we need to multiply the original count of bacteria by this factor:

Original number of bacteria × Growth factor = 26 × 23

Using the rules of exponents, when multiplying powers with the same base, you add the exponents:

26 × 23 = 26+3 = 29

Thus, the correct answer is B. 29.