Task 4: (D2) Calculus (exponential decay) (1) For a certain material, Newton's law of cooling can...

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Task 4: (D2) Calculus (exponential decay) (1) For a certain material, Newton's law of cooling can be represented by the decay equation 0=25+90e -0.9t where t is the time in seconds. And 0 is the temperature (K) at any given 210 85. 569 54. 34. 22. $59 22 14. 9. 17 8.6 70 65 84 22 17 03 0 20 00 1275 813. 518. .26 14 330. 210. 134. 48 60 80 41 0 0.5 1.0 t 10 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6. 169 0 instant Complete the table then using appropriate software (or graph paper) plot e against tat 0.5s intervals for 0 t 6s (b) Determine the gradient of the tangent to the curve at t = 3 seconds, by:- (i) Drawing a tangent on the graph and (ii) by Differentiation. (iii) Comment on the results from (i) & (ii). Task 4: (D2) Calculus (exponential decay) (1) For a certain material, Newton's law of cooling can be represented by the decay equation 0=25+90e -0.9t where t is the time in seconds. And 0 is the temperature (K) at any given 210 85. 569 54. 34. 22. $59 22 14. 9. 17 8.6 70 65 84 22 17 03 0 20 00 1275 813. 518. .26 14 330. 210. 134. 48 60 80 41 0 0.5 1.0 t 10 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6. 169 0 instant Complete the table then using appropriate software (or graph paper) plot e against tat 0.5s intervals for 0 t 6s (b) Determine the gradient of the tangent to the curve at t = 3 seconds, by:- (i) Drawing a tangent on the graph and (ii) by Differentiation. (iii) Comment on the results from (i) & (ii).