Question

What are the steps to solving the temperature in two different ovens increased at a steady rate the temperature in of an age represented by the equation Y equals 25X 72 or X represents the number of minutes and Y represents the temperature in degrees Fahrenheit the temperature of oven be as shown in the graph compare the functions, initial values and rate of change then determine how much greater the temperature in oven be will be then oven after eight minutes

Answer 1

The equation for oven B is y = 38x + 72, with a higher rate of change than oven A (y = 25x + 72). After 8 minutes, oven B is 104 degrees Fahrenheit hotter.

To find the equation of the line for oven B using the points (1, 110) and (3, 186):

Slope (m):

Using the slope formula (m = (y2 - y1) / (x2 - x1)), where (x1, y1) = (1, 110) and (x2, y2) = (3, 186):

Slope (m) = (186 - 110) / (3 - 1) = 76 / 2 = 38.

Y-intercept (b):

Using the point-slope form (y - y1 = m(x - x1)) with the point (1, 110):

y - 110 = 38(x - 1)

Solving for y, we get y = 38x + 72.

So, the equation of the line for oven B is y = 38x + 72.

Now, comparing the functions for ovens A and B:

Initial values:

Oven A: y = 25x + 72 (initial value = 72)

Oven B: y = 38x + 72 (initial value = 72)

Both ovens have the same initial value of 72.

Rates of change:

Oven A: Slope = 25

Oven B: Slope = 38

The rate of change is higher for oven B (38) than for oven A (25).

To find the temperature difference after 8 minutes:

Oven A at x = 8:

y = 25(8) + 72 = 272

Oven B at x = 8:

y = 38(8) + 72 = 376

The difference is 376 - 272 = 104 degrees Fahrenheit.

Therefore, the temperature in oven B will be 104 degrees Fahrenheit greater than in oven A after 8 minutes.