Question

the graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number of days it is plugged into the wall current. which is a reasonable estimate of the constant of variation? 0.25 kwh per day 0.50 kwh per day 2.40 kwh per day 4.00 kwh per day

Explanation:

Step1: Understand the concept of constant of variation

For a direct - variation relationship \(y = kx\) (where \(y\) is electricity usage in kWh, \(x\) is the number of days, and \(k\) is the constant of variation), \(k=\frac{y}{x}\).

Step2: Estimate values from the graph

Looking at the graph, when \(x = 10\) days (approximate value from the grid), \(y=2.4\) kWh (approximate value from the graph).

Step3: Calculate the constant of variation

Using the formula \(k = \frac{y}{x}\), substitute \(y = 2.4\) and \(x = 10\). Then \(k=\frac{2.4}{10}=0.24\approx0.25\)

Answer:

\(0.25\) kWh per day