(1) Pollutants which don't degrade easily (DDT is an infamous example) have particularly long-lasting impacts on the environment. They can start by affecting a physical envi- ronment (air, soil, water), and then work their way up a food chain, often biogmanifying (increasing in concentration as they move up the chain). Recently, microplastic particles (MPs) have been detected in the human bloodstream [1], although it is a subject of ongoing research whether these biomagnify (a) If a person has a MP blood concentration of lµg/mL (micrograms per milliliter) in the year 2016, and it increases at a rate of 0.1µg/mL per year, give a function modelling their MP blood concentration as a function of the number of years that have passed since 2020. What are the slope and intercepts of this function? (b) In 2023, in the lakeside village of Bentown, the following functions each model a particular link (not in order) in the chain of MP contamination: (c) • Increase in tissue MP concentration in the lake's trout (in MP/g) is given by the function f(c) = 0.2c, where c is the lake concentration of MPs (in MP/L) • Increase in lake MP concentration (in MP/L) is given by the function g(p) = 0.01p, where Р is the town's yearly MP waste (in tonnes) • Increase due to trout consumption in human bloodstream MP concentration (in μg/mL) is given by the function h(t) 0.005√t, where t is the tissue concentration of MPs in the lake's trout (in MP/g) = Find and simplify a composition of the above functions which gives the increase due to trout consumption in human bloodstream MP concentration (in µg/mL) as a function of the town's yearly MP waste (in tonnes). What if we introduce bass to the food chain, which prey on the trout? Name some new functions (don't give them explicitly with numbers – just state their inputs and outputs, and their units), and compose them, so the input is the town's yearly MP waste (in tonnes), and the output is the increase due to bass consumption in human bloodstream MP concentration (in μg/mL). Suppose a water treatment plant is built on the lake to reduce MP con- centration. It reduces concentration continuously, at a constant rate of 0.01MP/L each day. However, at the start of each week (Day 1, 8, 15,...), BEN CO® dumps its waste in the lake, instantly increasing the concentration by 0.1MP/L. Let t represent the start (12am) of the tth day (so for example, t = 4.75 represents 6pm on the 4th day), and let the lake's concentration prior to this month start at 1MP/L. Sketch roughly what the graph of concentration c(t) as a function of time t would look like for the first 30 days (that is, let the y-axis be the start of Day 1). Do the following limits exist, and if so, what are their values? (d) 1.5 lim c(t), lim c(t), lim c(t) t→8- t→8+ t+8 If a person's blood concentration of MPs is given by the function h(t) 0.012, use the limit definition of a derivative to give the rate of change of concentration as a function of time t.