A respiratory cycle is defined as the beginning of one breath to the beginning of the next breath. The rate of air intake r (in L/sec) during a respiratory cycle for a physically fit male can be approximated by r t = 0.9 sin π 3.5 t , where t is the number of seconds into the cycle. A positive value for r represents inhalation and a negative value represents exhalation. a. How long is the respiratory cycle? b. What is the maximum rate of air intake? c. Graph one cycle of the function. On what interval does inhalation occur? On what interval does exhalation occur?
A respiratory cycle is defined as the beginning of one breath to the beginning of the next breath. The rate of air intake r (in L/sec) during a respiratory cycle for a physically fit male can be approximated by r t = 0.9 sin π 3.5 t , where t is the number of seconds into the cycle. A positive value for r represents inhalation and a negative value represents exhalation. a. How long is the respiratory cycle? b. What is the maximum rate of air intake? c. Graph one cycle of the function. On what interval does inhalation occur? On what interval does exhalation occur?
A respiratory cycle is defined as the beginning of one breath to the beginning of the next breath. The rate of air intake
r
(in L/sec) during a respiratory cycle for a physically fit male can be approximated by
r
t
=
0.9
sin
π
3.5
t
, where
t
is the number of seconds into the cycle. A positive value for
r
represents inhalation and a negative value represents exhalation.
a. How long is the respiratory cycle?
b. What is the maximum rate of air intake?
c. Graph one cycle of the function. On what interval does inhalation occur? On what interval does exhalation occur?
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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