The blood pressure p for a certain individual follows a pattern of simple harmonic motion during the pumping cycle between heartbeats. The minimum pressure is 80 mmHg (millimeters of mercury) and the maximum pressure is 120 mmHg. The individual's pulse is 60 beats per minute or equivalently 1 beat per second. Write a model representing the blood pressure p at a time t seconds into the cycle. Assume that at t = 0 , the blood pressure is 100 mmHg and is initially increasing.
The blood pressure p for a certain individual follows a pattern of simple harmonic motion during the pumping cycle between heartbeats. The minimum pressure is 80 mmHg (millimeters of mercury) and the maximum pressure is 120 mmHg. The individual's pulse is 60 beats per minute or equivalently 1 beat per second. Write a model representing the blood pressure p at a time t seconds into the cycle. Assume that at t = 0 , the blood pressure is 100 mmHg and is initially increasing.
Solution Summary: The author explains the model that represents the blood pressure, p (in mmHg), as a function of time, and the origin of the graph is shifted vertically to the midpoint of maximum and minimum
The blood pressure
p
for a certain individual follows a pattern of simple harmonic motion during the pumping cycle between heartbeats. The minimum pressure is
80
mmHg (millimeters of mercury) and the maximum pressure is
120
mmHg. The individual's pulse is
60
beats per minute or equivalently
1
beat per second. Write a model representing the blood pressure
p
at a time
t
seconds into the cycle. Assume that at
t
=
0
, the blood pressure is
100
mmHg and is initially increasing.
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
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