Question

The equation yˆ=−0.37x^2+6.15x+52.3 approximates the average temperature in October in degrees Fahrenheit at an agricultural community x hours after 5 a.m.What is the best estimate for the average temperature in October at 9 a.m.?64°F67°F71°F78°F

Answer 1

So we have the equation:

`y=-0.37x^2+6.15x+52.3`

Where x represents the hours passed after 5 am and y represents the temperature in degrees Fahrenheit. We are being asked about the temperature at 9 am so we need to express 9 am in terms of hours passed after 5 am. Since there's a difference of 4 hours between this two times then we must use x=4 and the result of substituting x by 4 in the former equation will give us the temperature we are looking for:

`y_((4))=-0.37\cdot4^2+6.15\cdot4+52.3=70.98`

So the temperature in october at 9 am is 70.98°F so the best approximation would be option C, 71°F.