Question

the graph shows the relationship between time, in hours, and the population, in thousands, of a culture of bacteria. which statement describes the meaning of the point (0, 10) on the graph?
a. after 10 hours, there are 10,000 bacteria.
b. after 10 hours, there are no more bacteria.
c. the population began with 10,000 bacteria.
d. the population is multiplying itself by 10 each hour.

Explanation:

To determine the meaning of the point \((0, 10)\) on the graph, we analyze the axes: the x - axis represents time (in hours) and the y - axis represents the population (in thousands of bacteria). When \(x = 0\) (time = 0 hours, which is the start time), \(y=10\). Since the y - value is in thousands of bacteria, this means the initial population (at time 0) is \(10\times1000 = 10000\) bacteria.

• Option A: When \(x = 10\), we are not looking at \(x = 0\), so this is incorrect.
• Option B: The y - value is 10 (thousand), not 0, so there are bacteria, and this is incorrect.
• Option C: At \(x = 0\) (start), \(y = 10\) (thousand), so the population began with 10,000 bacteria. This is correct.
• Option D: The point \((0,10)\) does not give information about the rate of multiplication per hour, so this is incorrect.

Answer:

C. The population began with 10,000 bacteria.