Final answer:
To find the population 978 minutes from now, divide 978 by the doubling time and double the population the resulting number of times.
Step-by-step explanation:
To find the population 978 minutes from now, we need to determine how many times the population doubles in that time period. We can divide 978 by the doubling time of 163 minutes to find the number of doubling periods. 978 minutes ÷ 163 minutes = 6 doubling periods.
Since the initial population is 55,700, we can simply double the population 6 times to find the population after 978 minutes.
- 1st doubling: 55,700 × 2 = 111,400
- 2nd doubling: 111,400 × 2 = 222,800
- 3rd doubling: 222,800 × 2 = 445,600
- 4th doubling: 445,600 × 2 = 891,200
- 5th doubling: 891,200 × 2 = 1,782,400
- 6th doubling: 1,782,400 × 2 = 3,564,800
Therefore, the population will be approximately 3,564,800 bacteria 978 minutes from now.