You have been hired for a summer internship at a marine life aquarium. Part of your job is diluting brine for the saltwater fish tanks. The brine is composed of water and sea salt, and the salt concentration is 15.8% by mass, meaning that in any amount of brine the mass of salt is 15.8% of the total mass.
Using a calculator or spreadsheet we construct a table of values of \(S(x)\) from the expression for \(S(x)\) found in (b):
Number of half-liters | Salt concentration |
0 | 0.158 |
1 | 0.153 |
2 | 0.079 |
3 | 0.0632 |
4 | 0.0527 |
5 | 0.045 |
6 | 0.0395 |
7 | 0.035 |
The table shows that the salt concentration is very close to 4% when 6 half-liters (3 liters) of fresh water are added to the brine.
The solution to part (d) can be estimated from the graph found in (c) by drawing a horizontal line with vertical coordinate 0.04 and seeing what the value of \(x\) is where it intersects the graph of \(S\):