Question

The following problem represents a population of bacteria. P(1)-350(2)ᵗ where t equals time in hours. How many bacteria are present after 0, 1, and 2 hours? How do you know that the growth is not linear?

A. After 0 hours: 350, After 1 hour: 700, After 2 hours: 1400; The growth is exponential, not linear.
B. After 0 hours: 350, After 1 hour: 400, After 2 hours: 450; The growth is linear.
C. After 0 hours: 0, After 1 hour: 350, After 2 hours: 700; The growth is linear.
D. After 0 hours: 350, After 1 hour: 750, After 2 hours: 1150; The growth is exponential, not linear.

Answer 1

The number of bacteria present after 0, 1, and 2 hours is 350, 700, and 1400 respectively. The growth is exponential because the number of bacteria is increasing at an increasing rate.

Step-by-step explanation:

The problem represents a population of bacteria. The equation P(1)-350(2)ᵗ shows the number of bacteria present at different times, where t represents time in hours.

To find the number of bacteria present after 0, 1, and 2 hours, we substitute t=0, t=1, and t=2 into the equation. After 0 hours: 350 bacteria, after 1 hour: 700 bacteria, after 2 hours: 1400 bacteria.

The growth is exponential, not linear, because the number of bacteria is increasing at an increasing rate. In linear growth, the number of bacteria would increase by a constant amount at each time interval.