Forrest Lumber uses the function
S(t) = -75t + 375
to determine the salvage value S(t), in dollars, of a table saw t years after its purchase. How long will it take the saw to depreciate completely?
S(t) = -75t + 375
-75t + 375 = 0
-75t = -375
t = 5 years
Forgot to add the reasoning for setting the equation equal to 0.
Since S(t) is the salvage value, to find how many years it will take for the saw to depreciate, you would set the equation to 0.
This is because savage value would equal 0 dollars when an item was fully depreciated.
To determine how long it will take the table saw to depreciate completely, we can set the salvage value equation S(t) equal to zero, since a complete depreciation would mean the saw has no salvage value left.
The given salvage value function is:
S(t) = -75t + 375
Setting S(t) equal to zero, we have:
0 = -75t + 375
To solve this equation for t, we need to isolate the variable t on one side of the equation.
Adding 75t to both sides of the equation, we get:
75t = 375
Now, to isolate t, we divide both sides by 75:
t = 375/75
Simplifying the expression:
t = 5
Therefore, it will take the table saw 5 years to depreciate completely.