1. On the graph of f ( x ) = 8 sin ( 6 ? x ) , points P and Q are at consecutive

Question

1. On the graph of f(x)=8sin(6?x), points P and Q are at consecutive lowest and highest points with P occuring before Q. Find the slope of the line which passes through P and Q.
Slope =

2. A population of animals oscillates sinusoidally between a low of 300 on January 1 and a high of 1600 on July 1.  Graph the population against time and use your graph to find a formula for the population P as a function of time t, in months since the start of the year.  Assume that the period of P is one year.
P(t)=

Explanation / Answer

slope

minima at x = -1/3 f(x) = -8

maxima at x=1/3 f(x) = 8

hence slope = 16/(2/3)= 24

slope =24

p(t)= 950+650sin((pi/6)*t)

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