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 components

The total decrease is -20 in (negative as it's a decrease), the rate of decrease per week is -5 in (negative as it's a decrease per week).

Step2: Use the division formula interpretation

In the formula \(a\div b = c\), \(a\) is the total change (\(-20\)), \(b\) is the rate of change per unit time (\(-5\)), and \(c\) is the number of units of time. Here, \(c = 4\) represents the number of weeks it takes for the total decrease of \(20\) in (since \(\vert- 20\vert=20\) and \(\vert-5\vert = 5\)) to occur. So 4 is the time (in weeks) for the lake to decrease by 20 in.

Answer:

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