an empty swimming pool is shaped like a rectangular prism with a length of 18 feet and width of 9 feet. Once water begins to be pumped into the pool, the depth of the water increases at a rate of 0.5 foot hour. write a function d(t) that gives the depth in the pool after t hours
clearly, d(t) = 0.5t ft
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To write the function d(t) that gives the depth in the pool after t hours, we need to calculate the depth based on the rate at which the water is being pumped into the pool.
Given that the rate at which the depth increases is 0.5 foot per hour, we can use the equation:
d(t) = r × t,
where d(t) represents the depth of the water at time t, and r represents the rate of increase.
In this case, the rate of increase is 0.5 foot per hour. Therefore, the function becomes:
d(t) = 0.5t.
So, the function d(t) that gives the depth in the pool after t hours is:
d(t) = 0.5t.
To write the function d(t) that gives the depth in the pool after t hours, we need to consider the rate at which the water is being pumped into the pool.
The function d(t) represents the depth of the water in the pool after t hours. Since the initial depth of the pool is 0, the function can be defined as follows:
d(t) = 0.5t
This equation takes into account that the depth increases at a rate of 0.5 foot per hour and that the initial depth is 0.
For example, if we want to find the depth of the water after 3 hours, we can substitute t = 3 into the equation:
d(3) = 0.5 * 3 = 1.5 feet
Therefore, after 3 hours, the depth of the water in the pool would be 1.5 feet.