The population of koalas in a particular area varies according to the rule N(t) = 1000 + 200cos()
where N is the number of koalas and t is the number of months after 1 Jan 2013.
a. Find the amplitude and the period of the function N(t).
b. Find the maximum and minimum number of koalas in this area.
c. After how many months does the population of koalas become minimum for the first time?
d. Sketch the graph of N(t) over the first 24 months showing all axes intercepts and turning points correct to four decimal places.
e. Find the population of koalas after 10 months.
f. For how long does the population remain more than N(10), before it becomes less than N(10) again?

In the same area, the population of wombats varies according to the rule
P(t) = 1000 - 400sin()
where P is the number of wombats and t is the number of months after 1 Jan 2013.
g. When does the population of wombats become more than koalas?
h. How many more koalas than wombats are there in the area after 12 months?