The temperature of a chemical reaction oscilllates between a low of 40 degreesC and a high of 115degreesC. The temperature is at its highest point at the time t=0, and reaches its minimum point over a five-hour period. It then takes the same amount of time to return back to its initial temperature. Let y=H(t) denote the temperature of the reaction t hours after the reaction begins.  (a) What in the period of the function y=H(t)? __________ Include units in your answer.  (b) What in the midline of the function y=H(t)? __________ Include units in your answer. (c) What in the amplitude of the function y=H(t)? __________ Include units in your answer

The biologist has a second culture to examine. She knows that the population of the culture doubles every 15 minutes. After 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. 2. (a) What was the size of the initial population? Predict the size of the culture at t=3 hours. What was the size of the population at 40 minutes? Explain and justify your answers. (b) Create a graph of the population as a function of time. Find an equation that can be used to predict the size of the population at any time t. (c) Examine the rate at which the bacteria culture is growing. How fast growing after 1 hour? After 1.5 hours? After 2 hours? Use a time interval of h = 0.01 hours to estimate these rates. Interpret these rates in terms of the context of the problem situation. How do these three rates compare? (d) the culture

The fox population in a certain region has an annual growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 24400. (a) Find a function that models the population t years after 2000 (t = 0 for 2000). Your answer is P(t) = (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer should be an integer)

(UT) When you board a Ferris wheel moving counter- clockwise at a constant rate, your feet are 4 feet off the ground. At the highest point of the ride, your feet are 88 feet above the ground. It takes 220 seconds for the ride to complete one full revolution. Circle the correct values to create the correct function to model this situation, where t is time elapsed in seconds and h is height above the ground in feet. h (t) = c±a cos(bt) c = [ Select ] rt ±= [Select] a = [ Select ] b = [Select ]