Derive time dilation according to the theory of relativity

Damped waves are calculated according to the following formula:

Y (t) = e−kt sin (2t)

4.1 The current in an ac circuit at any time 𝑡 seconds is given by: 𝑖(𝑡) = 120 sin(100𝜋𝑡 +
0.36) amperes. Determine:
4.1.1 The peak value, the periodic time, the frequency and phase angle relative to
120 sin(100𝜋𝑡). 
4.1.2 The value of the current when 𝑡 = 0. 
4.1.3 The time when the current first reaches 60 A. 
4.1.4 The time when the current is first at maximum. 

Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially, there are 250
strands of the bacteria in the solution which grows to 800 strands after seven hours. Show (a) an
expression for the approximate number of strands in the culture at any time t and (b) the time needed for
the bacteria to grow to 1600 strands.