]. Submit your solutions in the submission link on the MATlMAB LMS page. 2. You submissions must be in a single pdffile in a good raolution. 3. Write your name and include the fol-lowing statement of originality: "This is my mm work. I have not copied any of it from anyone else" which must be signed and dated by you. 4. Written Assignment 1 will be marked out of ll): up to 9 marks will be awarded for your mathematics [the correctness of your solutions} and up to 1 mark will be awarded for your written communication (how well you have explained your answers]. Not everyI quation will be marked [quations that will be marked are chosen at random}. You will not be told which ones will be marked so you should attempt all quations. It is known that crustaceans can detect fluctuations in temperature with great precision. At low tide. in the intertidal zoneI temperatures can reach near-lethal levels for the intertidal crab Petrolisthes cfnctipes. These crabs tend to migrate to cooler microhabitats when temperatures get too high. It turns out that this behavioural response to temperature is likely triggered by a physio- logical response whereby thermosensitive neurons in the walking leg of P. ca'nctipes fire at a higher rates in higher temperatures. Min temperature of Temperature at voluntary movementI "C max firing rate. "C TI: 22 171.5 28 18.5 27 21 31.5 25 32 28 31 Source: E.K. Larn et al.. Frontiers in Physiology-13:?96125. 2022. o The vertical axis is Ty, the temperature which corrponds with the maximum rate of nerve firing in the walking legs of crabs. measured in degre Celsius. I The horizontal axis is TH. is the minimum temperature which corresponds to the voluntary movement of crabs to microhabitats with lower temperaturesI measured in degrees Celsius. a A model to describe the physiological response of P. cinctfpes vs their behavioural response to temperature is the linear model: no\") 13+ {1.5mi Show detailed calculations in all your answers using 2 decimal places of accuracy. Round off final answers of temperature calculations to one decimal place. 1. The minimum temperature of voluntary movement of a female crab was measured as 10C. Apply the linear model to estimate the temperature that corresponds with the maximum rate of nerve firing in the walking legs of this female crab. 2. The minimum temperature of voluntary movement of a male crab was measured as 20" C. Apply the linear model to estimate the temperature that corresponds with the maximum rate of nenre firing in the walking legs of this male crab. 3. Plot 1"}: as a function of T3 on the graph below using the domain: 5 E; I\" S. ill). 4. Compute T3425] and T3428] and compare them to he data in he table. 5. What value of TB will indicate that the temperature that corresponds with the max- imum rate of nerve firing is NFC? 6. Using the values from the table for the minimum temperature of voluntary movement TB = 7.5 and T's = 21, find the values of m and c in the linear model To = m*Tetc which agrees with these points. (Hint: the resulting linear model Tp = m * Ts + c should be close, but not necessarily exactly the same, to the one we used above). 7. Rearrange the equation Tp = 18 + 0.58T's so that T's is a function of Tp. Show each step of your working