Question

A rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. The rate r (in inches per hour) at which it rains is given by the function r= -0.5(t-1)+0.5 where t is the time (in hours).

A] For how long does it rain?

Options:
A) 1 hour
B) 2 hours
C) 3 hours
D) 4 hours

Answer 1

The rainstorm lasts for 2 hours.

Step-by-step explanation:

The rainstorm begins as a drizzle, which means that the rate of rain is increasing. Then it builds up to a heavy rain, which means that the rate of rain is at its highest. Finally, it drops back to a drizzle, which means that the rate of rain is decreasing. We can find the duration of the rainstorm by finding the time when the rate of rain becomes zero again.

The given function for the rate of rain is r = -0.5(t - 1) + 0.5 where t is the time in hours. To find when the rate of rain becomes zero, we set r equal to zero and solve for t:

0 = -0.5(t - 1) + 0.5

0 = -0.5t + 0.5 + 0.5

0 = -0.5t + 1

0.5t = 1

t = 2

Therefore, the rainstorm lasts for 2 hours.

Answer 2

Correct answer option B) 2 hours. By setting the rain rate function to zero and solving for time, it's determined that the rain lasts for 2 hours.

Step-by-step explanation:

To determine for how long it rains, we need to analyze the function describing the rain rate over time, given by r= -0.5(t-1)+0.5.

The rain rate r is measured in inches per hour, and t stands for time in hours. When the rain rate drops to zero, the rain stops.

Hence, we must find the value of t for which r = 0.

Setting r to zero and solving for t, we get:

• 0 = -0.5(t - 1) + 0.5
• 0 = -0.5t + 0.5 + 0.5
• 0.5t = 1
• t = 2

Therefore, the rainstorm lasts for 2 hours before the rain rate goes to zero, corresponding to answer option B) 2 hours.