Naturalists find that the populations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept when time t = 0 years. A minimum number of foxes, 200 foxes, occurred when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years. Researchers used this data to construct a function to model the population, p, as a function of time, t. The function they created is: :) + 500. P = 300 sin р 5л 11 -t 20л 11 Foxes are declared to be an endangered species when their population drops below 300. At what time t > 0 were the foxes first endangered? Round to the nearest tenth of a year. The foxes are never going to be endangered. 6.7 years 2.3 years 3.5 years

During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

A nationa! census is mandated by the Constitution of Pakistan to be held every ten years. After the independence of Pakistan in 1947, the first census took place in 1951. Figure 1 reflects the increase in population of Pakistan during last four nationa! census. The increase between 1972 and 2017 could be approximated by a linear function. If in 1972 the popuiation was 65.309 million and as per the census data of 2017 the popuiation was 207.774 million; a) Determine the estimation function P = f (t), where P equais the popuiation of Pakistan and t equals time measured in years since 1972. b) Interpret the slope and P intercept c) According to this function, what wii be the estimated popuiation of Pakistan in 2027 census? Census Data 250000000 200000000 150000000 100000000 50000000 1972 1981 1998 2017 Census Year Census Data Population (approx)

Sketch a rough graph of the number of hours of daylight asa function of the time of year.