When predator and prey populations cycle, the prey population can vary sinusoidally in time. The dynamics of a famous lynx-hare predator-prey cycle have been reconstructed from 1845 to 1935 based on the record of the number of pelts collected by the Hudson Bay Company. Here the number of hare pelts collected yearly,H(t)

H(t), oscillates sinusoidally with a 10 year cycle. The cycle has a minimum value of 5,000 and a maximum value of 50,000 pelts collected per year. Write down an equation forH(t)

H(t)as function of year, assuming that in 1848H(t)

H(t)was at it's lowest. Give the domain and range of the functionH(t)

H(t).

SECONG QUESTION

f(x)=1e^x and g(x)=x+x2

(a) whats the the domain off(x)

(b) Domain ofg(x)

(c) Find the domain of the composite functionfg

(d) Find the domain of the composite functiongf