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The initial concentration is 50mg/L, and underideal conditions, the concentration triples every three hours forthe first 15 hours. So, after 3 hours, the concentration will be50x3 = 150mg/LNow, let W be the weight and tbe the number of hours. Let, the required function model beW(t)=50 e^{k t}Then clearly, when t = 0, W = 50. Now, whent = 3, W = 150, soW(3)=150 \Rightarrow 50 e^{3 k}=150 \Rightarrow e^{3 k}=3 \Rightarrow k=\frac{\ln 3}{3}=0.366Thus, the function rule is given byW(t)=50 e^{0.366 t}Now, the given rate of tripling every three hours is valid onlyfor the first 15 hours, so the domain of thefunction is given byDomain W=[0,15]Now, clearly, W is an exponentially increasingfunction, and at t = 0, W = 50. So to find therange, we need to find the W when t =15, soW(15)=50 e^{0.366 \times 15}=50 \times 243=12150 \mathrm{mg} / \mathrm{L}So, range of W is given byRange W=[50,12150this completes part (a)Now, graphing the function we get ...