A biologist begins working with a sample containing 20,000 bacteria. The population size doubles every 10 days according to the equation, where \( t \) represents the number of days.

After seven days, the biologist begins working with a second sample of 20,000 bacteria. The equation used to represent the population of sample 2 after \( t \) days is .

Which of the following is an equivalent form of the equation for the population of sample 2?

1) \( P(t) = 20000 \times 2^{(t/10)} \)

2) \( P(t) = 20000 \times 2^{(t/7)} \)

3) \( P(t) = 20000 \times 2^{(7/t)} \)

4) \( P(t) = 20000 \times 2^{(10/t)} \)

The correct equation for the population of the second bacterial sample after t days, starting with the same initial amount and doubling every 10 days, is P(t) = 20000 * 2^(t/10).

Explanation:

The student is asking about an exponential growth model for bacteria population. The population of the first sample doubles every 10 days, and they start working with a second sample after 7 days with the same initial amount. Based on the context of exponential growth, the growth rate is applied from the point the second sample starts, not from when the first sample was begun. Therefore, the correct equation for the population of sample 2 after t days is P(t) = 20000 × 2(t/10) which corresponds to option 1.