Please show full solutions

Part 1

The population of geese in the Florida area which is represented by a periodic function. The population can be modelled by

(t)=1250sin0.1t+2000whereP is the geese population andt is the time in years.

a) What is the population's absolute minimum?

b) For how many years is the population less than the number 2625?

c) Over what period of time is the population growing?

Part 2

It takes 10 seconds to reach the top of a Ferris wheel with a radius of 18.5 meters.

a) Determine a sine function that represents the height, h, in meters, of the car relative to the ground as a function of the time, t, in seconds, if passengers board the lowest car at a height of 3 m above the ground.

Part 3

It is graphed for one period a) Determine the function's cosine equation for the following graph

b) What is the Amplitude, Period, Phase Shift and Vertical Shift