A video-on-demand service offers different streaming plans as shown in the given table. Determine, to the nearest cent, the rate of change in cost per minute of the video streaming.
We’re interested in the cost-per-minute rate of change. In the different plan options, the number of minutes you get goes up by 500 for each plan. How is the cost changing as the number of minutes go up by 500?
Well, from 42 to 58 is an increase of 16 dollars. From 58 dollars to 74 dollars is also an increase of 16 dollars. This is true for each step of the plan. What would be the rate of change of cost per minute?
There’s an increase of 16 dollars for every 500 minutes. If we divide the numerator and the denominator by 500, we’ll find out what the cost per minute is. If you divide 16 by 500, you get 0.032. Rounding to the nearest cent — we’d be rounding to the nearest hundredth — the nearest hundredth is three. Three hundredths in this case is three cents.
The rate of change is three cents per minute. There’s an increase of three cents per minute.