Week11a
Clicker Questions
Activities
Activity: tangent lines
Suppose we have the following information about the function $g(x)$:
$g(0)=0$, $g(1)=-1$, $g(2)=3$, $g(3)=2$, $g(4)=-2$ $g'(0)=1$, $g'(1)=2$, $g'(2)=0$, $g'(3)=4$, $g'(4)=-1$
Define a new function $h(x)=g(x^2-1)$. Find the equation of the line tangent to the graph of $h(x)$ at $x=2$.
Activity: various questions
Question: A ball is oscillating on the waves of the ocean and its height above the ocean floor after $t$ seconds is modelled by $h(t)=5+\sin{(t/2)}$.
- How fast the ball is travelling after 2 seconds?
- Is the ball moving up or down after 2 seconds? After 4 seconds?
- Is the velocity of the ball ever equal to 0?
Question:
The weight of a lake trout as a function of age is given by $W(t) = 25(1-e^{-0.2t})^3$, where W is weight in kilos and t is age in years. How fast is the trout's weight increasing when it is 1 year old? 2 years? (Later: Find the age at which the lake trout are increasing their weight most rapidly.)
Question:
At the time of the initial outbreak, the number of people with Ebola is 240 and the disease is spreading with the rate of $d(t)=240e^{t/3}$, where $t$ is days after the initial outbreak.
- How many people will have Ebola in 2 weeks?
- How fast is the disease spreading in 2 weeks?
Question:
You are taking a ride in a hot air balloon and your height is modelled by $h(t)=t+\sin{t}$ at time $t$ measured in minutes. The temperature at height $h$ is given by $T(h)=\dfrac{72}{1+h}$ degrees Fahrenheit.
- What is your temperature in 5 minutes?
- How fast is your temperature changing in 5 minutes? Is it dropping or rising?
Question:
The percent of people who have heard a certain rumour after $t$ hours is given by $R(t)=\dfrac{100}{1+2e^{-t}}$. How fast is the rumour spreading after 1 hour?
