While solar energy powered home systems are quite expensive to install, adding some passive energy features to conventional construction can make a substantial reduction in heating and cooling costs. Passive solar requires no machinery and uses the building itself to collect, store and distribute solar energy. An excellent passive solar investment is the installation of better quality windows with high resistance to heat transmission, provided with exterior shading on the south side to cut off high angled sun rays in cooling season and let in low angled winter sun during heating season.

Cor a typical conventional housing unit imporoved with better windows and south shading we can see the effect on heating, ventilating and air conditioning costs (HVAC)):

-cost of conventional HVAC system: $11300
-annual cost for HVAC in conventional house: $1290
-extra installation cost for better Windows & shading: $2600
-annual cost for HVAC in improved house: $840

CREATE EQUATIONS SHOWING TOTAL ACCUMULATED HVAC COST, CONVENTIONAL OVER N YEARS FOR THE CONVENTIONAL HOUSE, & TOTAL COST IMOROVED OVER N YEARS FOR THE IMPROVED HOUSE.

Conventional=__?__
Improved=__?__

To calculate the total accumulated HVAC cost over N years for both the conventional house and the improved house, we need to consider the annual cost for HVAC in each case.

Let's assume N represents the number of years.

For the conventional house:
Total accumulated HVAC cost over N years for the conventional house (C) = Annual cost for HVAC in conventional house × N

For the improved house:
Total accumulated HVAC cost over N years for the improved house (I) = Annual cost for HVAC in improved house × N + Extra installation cost for better windows & shading

Substituting the given values:
Annual cost for HVAC in conventional house = $1290
Annual cost for HVAC in improved house = $840
Extra installation cost for better windows & shading = $2600

Conventional house:
C = $1290 × N

Improved house:
I = $840 × N + $2600

Therefore, the equations showing the total accumulated HVAC cost over N years for the conventional house and the improved house are:
Conventional: C = $1290 × N
Improved: I = $840 × N + $2600