Drug Concentration The concentration C of a certain drug in a patient’s bloodstream t minutes after injection is given by C ( t ) = 50 t t 2 + 25 (a) Find the horizontal asymptote of C ( t ) . What happens to the concentration of the drug as t increases? (b) Using your graphing utility, graph C = C ( t ) . (c) Determine the time at which the concentration is highest.
Drug Concentration The concentration C of a certain drug in a patient’s bloodstream t minutes after injection is given by C ( t ) = 50 t t 2 + 25 (a) Find the horizontal asymptote of C ( t ) . What happens to the concentration of the drug as t increases? (b) Using your graphing utility, graph C = C ( t ) . (c) Determine the time at which the concentration is highest.
The graph below describes your height, h=f(t) , above the ground on a Ferris wheel, where h is in meters and t is time in minutes. You boarded the wheel before t=0 , and the boarding platform is level with the bottom of the wheel.
What is your position and direction at t=0?
You are at the 3 or 9 o'clock position, and ascending.You are at the 6 or 12 o'clock position, and descending.You are at the 3 or 9 o'clock position, and descending.You are at the 6 or 12 o'clock position, and ascending.
How long does it take the wheel to complete one full revolution?
What is the diameter of the wheel?
At what height above the ground do you board the wheel?
What is the length of time the graph shows you riding the wheel?
The red dashed line gives the cost C(x) and the
blue solid line gives the revenue R(x) in dollars.
4000
3900
3800
Reminder:
3700
The cost C(x) is the overall amount of money that a business
spends to produce x items. The revenue R(x) is the overall amount
of money that a business generates from producing and selling x
3600
3500
3400
3300
items.
3200
3100 -
(a) Use the graph of the blue solid line determine the following:
3000 -
The revenue if 200 items are sold. R(200) = $ Number
2900
2800
2700
2600
Find the formula for R(x).
R(x) =
2500
(b) Use the graph of the red dashed line to determine the
following:
2400
2300
2200 -
The cost to produce 50 items. C(50) = $ Number
2100 -
The cost to produce 250 items. C(250) = $ Number
у 2000
1900
Find the formula for C(x).
1800
C(x) =
1700
1600
(c) Complete the sentence:
1500 -
If 250 items are produced and sold then
1400
of $ Number
1300 -
1200
they have a
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(d) Use your formulas to find the coordinates of the break-even
point.
1100…
A ball is thrown in the air and its height is modeled by the function h(t)=-16(t-3)2+150, where h(t) is the height of the ball in feet and t is the time in seconds.
Will this graph be concave up or concave down? Explain your reasoning.
Sketch a graph for this function. On your graph, label the following:
Vertex
AOS
Y-intercept
The coordinate point that results when the y-intercept is reflected over the AOS
What is the maximum height the ball reaches?
How long does it take the ball to reach its maximum height?
Approximately how tall is the person throwing the ball?
Chapter 4 Solutions
Precalculus Plus MyLab Math with eText -- Access Card Package (10th Edition) (Sullivan & Sullivan Precalculus Titles)
Precalculus: Mathematics for Calculus (Standalone Book)
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