ENG1090: Foundation Mathematics Assignment, MUM, Malaysia Radioactive materials, such as Plutonium-239, Radium-226, and others, decay exponentially. The amount of radioactive material

Question 1.1

Radioactive materials, such as Plutonium-239, Radium-226, and others, decay exponentially. The amount of radioactive material present at time t can be described

where t represents time (in years), and R(t) represents the amount of radioactive material present at time t. After 700 years, a sample of Plutonium-239 has decayed to 40% of its original mass. Find the half-life of this sample of Plutonium-239, i.e., the amount of time it takes for Plutonium-239 to decay to half its original mass.

Question 1.2

Let d be the last non-zero digit of your student number. The average temperature of a machine is modelled by

where t is given in an hour.

a) Simplify the expression T(t) into an equivalent form , for constants
D, E, k. Hint: use the power reduction formulas introduced in Lecture 4.

b) Identify the period of the function T(t), and provide a brief reason for your answer.

c) Determine the amplitude A and the principal angle α when T(t) is written as a sine function in phase-angle form  Justify your answers carefully.

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