A homeowner installs a solar heating system, which generates 20 savings at a rate of 300e t dollars per year, t years after installation. Find a formula for the total savings after t years. If the system cost 30000 dollars to install, when will the savings match the installation cost

"35.84 years" is the appropriate solution.

Step-by-step explanation:

The given values are:

Rate of savings generation,

System cost to install,

= $30000

Now,

The total savings will be:

⇒  

On substituting the values, we get

⇒        

⇒  

When,

Savings = 0

t = 0, then

⇒  

⇒  

The formula will be:

⇒  

On putting the values in the above formula, we get

⇒  

On taking log, we get

⇒  

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3