Salinity, the concentration of salt in a body of water, is a crucial factor in the...

 

 

 

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Salinity, the concentration of salt in a body of water, is a crucial factor in the health of the local ecosystem. It is measured in parts per thousand (ppt), meaning grams of dissolved salt per thousand grams of water. For example, the salinity of the Chesapeake Bay varies from about 25 to 30 ppt near the Atlantic Ocean to less than 0.5 ppt near places where rivers flow into the Bay. (Source: Chesapeake Bay Foundation) Suppose the Chair of the Chesapeake Bay Foundation's Water Quality Goal Implementation Team, Captain Chesapeake, has heard of your mathematical expertise, and contacts you to analyze some data. Format your response as a letter to Captain Chesapeake. The measurements of the salinity at a certain location in the Bay are reported as follows: time salinity 2.0 ppt 1 year 10.0 ppt 2 years 16.0 ppt Let SS represent the salinity; it is a function of time tt in years. When you calculate salinities, express them to the nearest tenth of a ppt. Part (a) For part (a), find a quadratic model of salinity SS as a function of time tt that fits the observations given above. Use the general form of a quadratic function, S(t)=at2+bt+cS(t)=at2+bt+c. o For each salinity value given above, make appropriate substitutions into the quadratic function and simplify if possible; use the results to find the values of the unknowns in the quadratic function. Be sure to state the new equation obtained. Is it possible to find more than one quadratic model that fits the data perfectly? Explain. • Use your quadratic model to predict the salinity at t=3t=3 years. Use desmos.com to make a large graph of your quadratic model, at least through t=10t=10 years. Your graph must contain realistic values - example: time cannot be negative. • Use your quadratic model to predict the long-term trend of salinity. That is, what do you expect to happen in the future in terms of the salinity in this model? Identify any points of interest if applicable within this range. Salinity, the concentration of salt in a body of water, is a crucial factor in the health of the local ecosystem. It is measured in parts per thousand (ppt), meaning grams of dissolved salt per thousand grams of water. For example, the salinity of the Chesapeake Bay varies from about 25 to 30 ppt near the Atlantic Ocean to less than 0.5 ppt near places where rivers flow into the Bay. (Source: Chesapeake Bay Foundation) Suppose the Chair of the Chesapeake Bay Foundation's Water Quality Goal Implementation Team, Captain Chesapeake, has heard of your mathematical expertise, and contacts you to analyze some data. Format your response as a letter to Captain Chesapeake. The measurements of the salinity at a certain location in the Bay are reported as follows: time salinity 2.0 ppt 1 year 10.0 ppt 2 years 16.0 ppt Let SS represent the salinity; it is a function of time tt in years. When you calculate salinities, express them to the nearest tenth of a ppt. Part (a) For part (a), find a quadratic model of salinity SS as a function of time tt that fits the observations given above. Use the general form of a quadratic function, S(t)=at2+bt+cS(t)=at2+bt+c. o For each salinity value given above, make appropriate substitutions into the quadratic function and simplify if possible; use the results to find the values of the unknowns in the quadratic function. Be sure to state the new equation obtained. Is it possible to find more than one quadratic model that fits the data perfectly? Explain. • Use your quadratic model to predict the salinity at t=3t=3 years. Use desmos.com to make a large graph of your quadratic model, at least through t=10t=10 years. Your graph must contain realistic values - example: time cannot be negative. • Use your quadratic model to predict the long-term trend of salinity. That is, what do you expect to happen in the future in terms of the salinity in this model? Identify any points of interest if applicable within this range.