High School

Suppose a leak develops in a pipe, and water leaks out of the pipe at the rate of [tex]L(t) = 0.5t + 3[/tex] liters per hour, [tex]t[/tex] hours after the leak begins.

1. How much water will have leaked out after 4 hours?
2. Suppose the pipe leaks for [tex]t[/tex] hours. Find the total amount of water leaked.

Answer :

Final answer:

The leakage rate after 4 hours, calculated using the provided formula L(t) = 0.5t + 3, is 5 liters. The total water leakage after time 't' can also be determined with the same formula.

Explanation:

The question revolves around a pipe leakage represented by the formula L(t) = 0.5t + 3, which indicates the amount of water leaked (in liters) per hour (in time 't'). To find the amount of water leaked after 4 hours, you simply substitute 't' with '4' in your equation.

According to the formula, L(4) = 0.5*4 + 3 = 2 + 3 = 5 liters. So, after 4 hours, 5 liters of water will have leaked. This is the water leakage rate. To find the total amount of water that leaked out after time 't', again substitute 't' in the equation L(t) = 0.5t + 3. That is the water leakage volume.

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