Horizon BP in Antelope Park, Alaska, has noticed that utility bills are substantially higher when the average monthly temperature is colder. The only thing in the shop that uses natural gas is the furnace. Because of prevailing low temperatures, the furnace is used every month of the year $($though less in the summer months and very little in August$).$ Everything else in the shop runs on electricity, and electricity use is fairly constant throughout the year.

For a year, Horizon has been recording the average daily temperature and the cost of its monthly utility bills for natural gas and electricity.

Average Temperature Utility Cost

January $31\backslash$deg F $ $764$

February $41633$

March $43547$

April $44414$

May $46279$

June $50237$

July $53224$

August $60214$

September $50309$

October $40534$

November $30754$

December $10884$

Required:

Use the high$-$low method to estimate utility cost for the upcoming months of January and February. The forecast for January is a near record average temperature of $5\backslash$deg F; temperatures in February are expected to average $40\backslash$deg F$.$Horizon BP in Antelope Park, Alaska, has noticed that utility bills are substantially higher when the average monthly temperature is

colder. The only thing in the shop that uses natural gas is the furnace. Because of prevailing low temperatures, the furnace is used

every month of the year $($though less in the summer months and very little in August$).$ Everything else in the shop runs on electricity,

and electricity use is fairly constant throughout the year.

For a year, Horizon has been recording the average daily temperature and the cost of its monthly utility bills for natural gas and

electricity.

Required:

Use the high$-$low method to estimate utility cost for the upcoming months of January and February. The forecast for January is a near

record average temperature of $5F$; temperatures in February are expected to average $40F.$