7. An influenza virus is spreading through a school according to the function N(t) = 3(2)^t, where N is the number of people infected and t is the time, in days.
a) How many people have the virus initially, when t = 0?
b) Determine the average rate of change between
i) day 1 and day 2 ii) day 2 and day 3
4. Given f(x) = 1/x
and g(x) = sinx, provide a characteristic that the two functions have in common and a characteristic that distinguishes them.
5. Describe the difference between finding the average rate of change and the instantaneous rate of change. How are they related to secants and tangents? Use a diagram to help you explain.
6. a) Given f(x) = log(x) and g(x) = 1 /(𝑥+3), identify the steps you would take to determine the domain of (f ∘ g)(x). What is the domain of (f ∘ g)(x)?
b) Would the domain of (g ∘ f)(x) be the same? Explain.Mathematics2 months ago
A large wheel is attached to a boat and spins as the boat moves. A rock becomes nudged in the wheel as it spins in the water. It is noticed that at t = 2 s, the rock is at the highest point 3 m above the water. At time t = 6 seconds, the rock is submerged in the water 5 m below the water(the lowest point).
a. Graph 5 points to represent one cycle of the above problem. Label these points clearly on your graph.
b. Determine a cosine model to represent the motion of the wheel.
c. Determine whether the rock was above the water’s surface at t = 0 or below the water’s surface and how far is the rock above or below the water at this time?2 AnswersPhysics2 months ago
Junala substituted x =π/2 into the expression. 4sinx + sin^(2) x + cos^(2) x = 5 and saw the following: 4 sin (π/2) + cos^2 (π/2) + sin^2 (π/2) = 5 and concluded this was a trig identity. Is Junala correct? Provide a brief explanation of Junala’s thought process.
1. Suppose you wanted to model a Ferris wheel using a sine function that took 60 seconds to complete one revolution. The Ferris wheel must start 0.5 m above ground.
Provide an equation of such a sine function that will ensure that the ferris wheel’s minimum height of the ground is 0.5 m.
Explain why your equation works.
Students participating in a psychology experiment and took MHF4U were given an exam. Every month for a year after the exam, the students were retested to see how much of the material they remembered. The average scores for the group are given by the human memory model: f(t)=75 - (6log(t+1))/(log e) where e is the number in your calculator and t is time in months 0< t < 12.
a) What was the average score on the original exam (t=0)
b) When was the average score equal to 61.2%