Question

the height of a lake decreases by 20 in over a period of time. the height decreases by 5 in each week. the equation below is written to represent the situation: -20 ÷ (-5) = 4 which description best explains the meaning of 4 in the equation? a the new height of the water in the lake is 4 in. b the change in the height of the lake is 4 in. c the time it takes for the lake to decrease in height by 5 in is 4 weeks. d the time it takes for the lake to decrease in height by 20 in is 4 weeks.

Explanation:

Step1: Analyze the equation

The equation \(-20\div(-5) = 4\) is based on the formula \(time=\frac{total\ change}{rate\ of\ change}\). Here, the total change in height is \(- 20\) inches (negative because it's a decrease) and the rate of change is \(-5\) inches per week (negative because the height is decreasing each week).

Step2: Interpret the result

When we calculate \(\frac{-20}{-5}\), we are finding out how many weeks (\(4\)) it takes for the height of the lake to decrease by \(20\) inches at a rate of \(5\) inches per week.

Answer:

D. The time it takes for the lake to decrease in height by 20 in is 4 weeks.