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 \(-20\div(-5) = 4\) represents the relationship between the total decrease in height (\(-20\) inches, negative because it's a decrease), the rate of decrease per week (\(-5\) inches per week, negative because it's a decrease), and the time.

Step2: Use the formula for rate of change

The formula for rate of change is \(\text{time}=\frac{\text{total change}}{\text{rate of change}}\). Here, \(\text{total change}=- 20\) (total decrease in height of the lake) and \(\text{rate of change}=-5\) (decrease per week). When we calculate \(\frac{-20}{-5}\), we are finding the time it takes for the total decrease of \(20\) inches (since \(\vert-20\vert = 20\) and \(\vert-5\vert=5\)) 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.