A weather forecast predicts that the temperature in antarctica will decrease 8 degrees fahrenheit each hour for the next 6 hours. write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36 degrees fahrenheit

Given:

m = - 8 degrees/hour, the rate of change of temperature

Let x = hours

Let y = temperature, °F

Then y = - 8x + b

where b = constant

When x = 0, then y = b.

Therefore b = initial temperature

If the temperature drops by at least 36 °F in the next x hours, then

b - y (6) ≥ 36

b - (-8x + b) ≥ 36

8x ≥ 36

x ≥ 4.5 hours

Answer: At least 4.5 hours