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 writ 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 problem

We have a total decrease in height of \(20\) inches (\(- 20\)) and a rate of decrease of \(5\) inches per week (\(-5\)). The formula used is \(\text{time}=\frac{\text{total change}}{\text{rate of change}}\).

Step2: Interpret the formula

In the equation \(-20\div(-5) = 4\), \(-20\) is the total decrease in height (negative because it's a decrease), \(-5\) is the rate of decrease per week (negative because height is decreasing). When we divide the total decrease by the rate of decrease, we get the time.

Answer:

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