Question

multiple choice
identify the choice that best completes the statement or answers the question.

1. this table shows the number of swimmers in the ocean at a given time. find the rate of change for each time period. during which period did the number of swimmers increase at the fastest rate?

time	10:30 am	12:30 pm	1:30 pm	3:30 pm	5:30 pm

a. between 10:30 and 12:30; 7 \\(\frac{\text{swimmers}}{\text{hour}}\\) c. between 12:30 and 1:30; 9 \\(\frac{\text{swimmers}}{\text{hour}}\\)
b. between 3:30 and 5:30; 5 \\(\frac{\text{swimmers}}{\text{hour}}\\) d. between 1:30 and 3:30; 3 \\(\frac{\text{swimmers}}{\text{hour}}\\)

Explanation:

Step1: Calculate time difference (10:30-12:30)

Time elapsed: $12:30 - 10:30 = 2$ hours

Step2: Compute rate (10:30-12:30)

Rate: $\frac{55 - 41}{2} = \frac{14}{2} = 7$ $\frac{\text{swimmers}}{\text{hour}}$

Step3: Calculate time difference (12:30-1:30)

Time elapsed: $1:30 - 12:30 = 1$ hour

Step4: Compute rate (12:30-1:30)

Rate: $\frac{64 - 55}{1} = 9$ $\frac{\text{swimmers}}{\text{hour}}$

Step5: Calculate time difference (1:30-3:30)

Time elapsed: $3:30 - 1:30 = 2$ hours

Step6: Compute rate (1:30-3:30)

Rate: $\frac{70 - 64}{2} = \frac{6}{2} = 3$ $\frac{\text{swimmers}}{\text{hour}}$

Step7: Calculate time difference (3:30-5:30)

Time elapsed: $5:30 - 3:30 = 2$ hours

Step8: Compute rate (3:30-5:30)

Rate: $\frac{80 - 70}{2} = \frac{10}{2} = 5$ $\frac{\text{swimmers}}{\text{hour}}$

Step9: Compare all rates

Rates: $7, 9, 3, 5$. The largest is 9.

Answer:

c. Between 12:30 and 1:30; 9 $\frac{\text{swimmers}}{\text{hour}}$