SOLUTION: The weather bureau has determined that for the 10 hours after midnight in a particular storm the relationship between the time elapsed since midnight and the water level for a part

Question 1128825: The weather bureau has determined that for the 10 hours after midnight in a particular storm the relationship between the time elapsed since midnight and the water level for a particular river is a linear relationship and can be described by a linear function. If we let 𝑡𝑡 represent the time elapsed in hours since midnight and let ℎ be the water level measured in inches, the relationship is given by
ℎ = 95 + 2𝑡.
a. What is the level of the river at midnight?

b. What is the level of the river at 3:00 am ?

c.We see that ℎ is a linear function of 𝑡. What is the domain of this function?
d. Identify the rate of change in this equation and give a physical interpretation of that rate of change, i.e., an interpretation within the context of the problem. Your physical interpretation should be expressed in one or more complete sentences. Be sure to include units where appropriate in the physical interpretation.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
a. t=0 at midnight so level is 95 inches
b. t=3 at 3 am, so the level is 95+6=101 inches.
c. The domain is [0, 10], since the function is valid for 10 hours after midnight.
d. The rate of change is 2 inches/hour and it means that the river is rising at 2 inches per hour for up to 10 hours after midnight.
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