The owner of a commercial fishing operation decides to upgrade the hydraulic pumps, hydraulic lines, and the drum drive to a new system that is supposed to save costs over time. The projected savings rate for the new equipment is given by S′(x)=225−x2S′(x)=225−x2
Here is the given information:
The owner of a commercial fishing operation decides to upgrade the hydraulic pumps, hydraulic lines, and the drum drive to a new system that is supposed to save costs over time. The projected savings rate for the new equipment is given by
S′(x)=225−x2S′(x)=225−x2
where xx is the number of years the machinery will be used.
The rate of additional costs to run and maintain the new equipment is expected to be
C′(x)=x2+25x+150C′(x)=x2+25x+150
Both functions have units of thousands of dollars per year.
1.1
Graph both of the rate functions on the same page in Desmos.
Make sure to adjust your graph display settings so that the appropriate domain and range are used.
Share your graph using a link.
1.2
What is the appropriate domain and range for these functions?
FYI: The domain will be the same for both (the range will not be the same, though).
1.3
For which xx does S′(x)=C′(x)S′(x)=C′(x)? Solve the equation algebraically.
What point on the graph does the solution correspond to?
What does a solution here mean in the context of this problem?
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