Question 1
For Australia, the growth in population from the year 1990 can be approximated by the equation
P(t) = 17e0.0108t
where P(t) is the population in millions of people and t is time in years from the year 1990.
(a) What was the approximate population in 1990 (t = 0)?
(b) Using equation 1, calculate the approximate population for the year 2015 (t = 25).
(c) According to equation 1, in what year will the Australian population reach 30 million?
Question 2
In the electrical circuit shown in figure1, there is a self induced back electromotive force (emf) which opposes the change in current and
remains until the current in amperes increases from 0 to its final value, Vs/R . The circuit current at any time is:
where Vs is the Supply voltage in volts, R the circuit resistance in ohms, L the circuit inductance in henry and t is time in seconds.
Show how the inductance, L in?uences the current, I by sketching two curves of the current versus the time for a high circuit inductance, 1 H and a low circuit inductance, 10-3 H. Note that the self induced emf will always be less than the supply voltage so your current curves will never fall below 0 but will both reach a maximum limit of Vs.