The initial value of the function for oven A is 72, and the rate of change is 25. The initial value of the function for oven B is 110, and the rate of change is 38. After 8 minutes, the temperature in oven B will be 142 degrees Fahrenheit greater than oven A.
The temperature in oven A is represented by the equation y = 25x + 72, where x represents the number of minutes and y represents the temperature in degrees Fahrenheit. The initial value of the function is 72, as this is the y-intercept. The rate of change, or slope, is 25, which means that for every increase of 1 minute, the temperature increases by 25 degrees Fahrenheit.
The temperature in oven B can be determined from the given graph. Let's use the coordinates (1, 110) and (3, 186) to find the slope. The change in y is 186 - 110 = 76, and the change in x is 3 - 1 = 2. Therefore, the rate of change for oven B is 76/2 = 38 degrees Fahrenheit per minute.
To determine how much greater the temperature in oven B will be than oven A after 8 minutes, we can calculate the temperature for each oven using their respective equations. For oven A, y = 25(8) + 72 = 272 degrees Fahrenheit. For oven B, y = 38(8) + 110 = 414 degrees Fahrenheit. Therefore, the temperature in oven B will be 414 - 272 = 142 degrees Fahrenheit greater than oven A after 8 minutes.