The amount of snowfall is a function of time
Beginning at midnight, meteorologists record the snowfall in inches per hour.What is the best interpretation for the following statement? Use appropriate units.
Interpret the values in the context of the problem stated.
Polly Hedron wants to lose weight from the holidays. Her weight gain/loss can be modeled by 𝑃(𝑡), where p is measured in pounds per week and t is weeks since she started her diet. Interpret 𝑃′(6) = −1.3
t (minutes) | 0 | 5 | 10 | 15 | 20 |
|---|---|---|---|---|---|
S(t) (degree F) | 138 | 115 | 104 | 95 | 87 |
The temperature of chicken soup at time t is modeled by a strictly decreasing, twice differentiable function S, where S(t) is measured in degrees Fahrenheit and ¢ is measured in minutes. The soup is cooling for 20 minutes, beginning at t = 0. Values of S(t) at selected times t are given in the table above. Use the data in the table to estimate S’(4). Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem.
Wheat is being poured into a cylindrical silo with a radius of 4 inches so that the height of the wheat is increasing at a constant rate of 0.5 inches per second. At what rate is the volume of the wheat in the silo increasing at the instant when the height is the same as the radius?
The following function gives the population of an endangered tortoise species in thousands, 𝑡 years after biologists surveyed the habitat:
What is the instantaneous rate of change in the turtle population, 6 years after the survey. Include proper units.
The amount 𝐴(𝑡) of widgets produced by a manufacturer is given by the function
where 𝑡 is the number of hours of production since the start of the day at 7:00 am. At what time(s) is the rate of production the greatest?
The radius 𝑟 of a spherical weather balloon is increasing at the uniform rate of 0.4 inch per minute. At the instant when the surface area 𝑆 becomes 100𝜋 square inches, what is the rate of increase in the volume 𝑉? Include appropriate units.
The table below gives selected values of a twice-differentiable function f(x).
x | -5 | -3 | -1 | 1 | 3 |
|---|---|---|---|---|---|
f(x) | 0 | 3 | 1 | 2 | 0 |
f'(x) | -3 | -2 | -1 | 1 | -4 |
Find
Find the following. Use L’Hospital’s Rule when possible.
Find the following. Use L’Hospital’s Rule when possible.
Find the limit, use L'Hospital's Rule, if necessary
A manufacturer has a monthly fixed cost of $175,000 and a production cost of $20 for each unit produced. The product sells for $32 per unit.
What is the cost function, C(x) ?
What is the revenue function, R(x)?
What is the profit function, P(x)?
How many units should the company produce in order to make a profit of $50,000?