Question

(1 point) Lakes receive water from streams each year and lose water to outflowing streams (Ignore evaporation for this problem). The following values are based on the Great Salt Lake in Utah. The lake receives (inflow during the year) 3⋅106m3 of water per year with salinity of 1 parts per thousand. The phrase 1 part per thousand means for every 1000 cubic meters of water there is 1 cubic meter of salt. The lake contains 3.3⋅107m3 of water and starts with no salinity. The lake loses 3⋅106m3 water each year (outflow). Assume that the water that flows out (during a year) has a concentration equal to that of the entire lake on January 1st of each year. Do not take into account the new saltwater entering when trying to figure out the concentration of the water exiting the lake. Essentially assume the lake drains first and then the new saltwater comes later in the year. Now answer the following questions: a) : The total amount of salt in the lake after a year is equal to 3000 (start from January 1st). b) : The concentration of salt in the lake after a year is equal to . c) : The total amount of salt in the lake after a second year if there is outflow but no inflow during the second year is equal to . d) : The total amount of salt in the lake after a second year if there is inflow but no outflow during the second year is equal to 6000 . e) : The total amount of salt in the lake after a second year if there is both inflow and outflow during the second year is equal to . f) : The concentration of salt in the lake after a second year if there is both inflow and outflow during the second year is equal to . g) : Write a DTDS that compares the concentration of salt at time t to the concentration of salt 1 year later: c1 = (we use denotations c0 and c1 for concentrations at time t and a year after, i.e. find formula for c1 in terms of c0).

Answer 1