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 is - 5 in per week (negative as it's a decrease).

Step2: Use the formula \(t=\frac{\text{total change}}{\text{rate of change}}\)

Here, \(t = - 20\div(-5)\). The result 4 represents the time. Since the total decrease is 20 in (magnitude) and rate is 5 in per week (magnitude), 4 is the time for 20 in decrease.

Answer:

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