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 total decrease in height is \(20\) in (represented as \(- 20\) since it's a decrease), and the rate of decrease per week is \(5\) in (represented as \(-5\) since it's a decrease). The formula \(\text{time}=\frac{\text{total change}}{\text{rate of change}}\).

Step2: Interpret the result

When we calculate \(-20\div(-5)\), we are finding the number of weeks it takes for the height to decrease by \(20\) in at a rate of \(5\) in per week.

Answer:

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