Question

the following situation involves a rate of change that is constant. write a statement that describes how one variable changes with respect to the other, give the rate of change numerically (with units), and use the rate of change rule to answer any questions.
snow accumulates during a storm at a constant rate of 2.7 inches per hour. how much snow accumulates in the first 6.2 hours? in the first 8.2 hours?
which statement describes this situation?
a. the snow accumulated varies with respect to time with a rate of change of 2.7 in/h.

b. time varies with respect to the snow accumulated with a rate of change of 2.7 h/in.

c. the snow accumulated varies with respect to time with a rate of change of 2.7 h/in.

d. time varies with respect to the snow accumulated with a rate of change of 2.7 in/h.
how much snow has accumulated after the first 6.2 hours?
inches
(type an integer or a decimal.)

Explanation:

Step1: Identify the relationship

The snow accumulation (let's call it \( S \)) depends on time ( \( t \) ) with a rate of change (slope) of \( 2.7 \) inches per hour. The formula for constant rate of change is \( S = r \times t \), where \( r = 2.7 \) in/h and \( t \) is time in hours.

Step2: Calculate for 6.2 hours

Substitute \( t = 6.2 \) hours and \( r = 2.7 \) in/h into the formula:
\( S = 2.7 \times 6.2 \)
Calculate the product: \( 2.7 \times 6.2 = 16.74 \)

Step3: Calculate for 8.2 hours (optional, but part of the question)

Substitute \( t = 8.2 \) hours:
\( S = 2.7 \times 8.2 \)
Calculate the product: \( 2.7 \times 8.2 = 22.14 \) (though the question here focuses on 6.2 hours first)

Answer:

For the first part (statement): A. The snow accumulated varies with respect to time with a rate of change of 2.7 in/h.
For the snow after 6.2 hours: \( 16.74 \) inches.