Final answer:
After 0, 1, and 2 hours, the bacteria population calculated using the exponential growth formula P(t) = 350(2)ᵗ is 350, 700, and 1400, respectively. This indicates exponential growth since the amount of bacteria doubles at each time interval.
Step-by-step explanation:
The problem you’ve posed involves a formula for exponential growth: P(t) = 350(2)ᵗ, where P(t) represents the population of bacteria at time t, measured in hours. To determine how many bacteria are present after 0, 1, and 2 hours, we simply plug those values of t into our formula.
- After 0 hours: P(0) = 350(2)⁰ = 350(1) = 350
- After 1 hour: P(1) = 350(2)¹ = 350(2) = 700
- After 2 hours: P(2) = 350(2)² = 350(4) = 1400
To explain why the growth is not linear, we observe the rate of change between hours. In linear growth, this rate is constant, meaning the same number of bacteria would be added each hour. However, in exponential growth, the rate of change increases; the population doubles each hour. Thus, the correct answer is a) After 0 hours: 350, 1 hour: 700, 2 hours: 1400. The growth is exponential.