Technology Exercises Response of a Muscle When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the form R ( x ) = 100 x b + x , x ≥ 0 , where x is the concentration of acetylcholine (in appropriate units), b is a positive constant that depends on the particular frog, and R ( x ) is the response of the muscle to the acetylcholine, expressed as a percentage of the maximum possible effect of the drug. Suppose b = 15 . Find the response of the muscle when x = 30 . Determine the value of b if R ( 50 ) = 30 ; that is, if a concentration of x = 50 units produces a 30 % response.
Technology Exercises Response of a Muscle When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the form R ( x ) = 100 x b + x , x ≥ 0 , where x is the concentration of acetylcholine (in appropriate units), b is a positive constant that depends on the particular frog, and R ( x ) is the response of the muscle to the acetylcholine, expressed as a percentage of the maximum possible effect of the drug. Suppose b = 15 . Find the response of the muscle when x = 30 . Determine the value of b if R ( 50 ) = 30 ; that is, if a concentration of x = 50 units produces a 30 % response.
Response of a Muscle When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the form
R
(
x
)
=
100
x
b
+
x
,
x
≥
0
,
where
x
is the concentration of acetylcholine (in appropriate units),
b
is a positive constant that depends on the particular frog, and
R
(
x
)
is the response of the muscle to the acetylcholine, expressed as a percentage of the maximum possible effect of the drug.
Suppose
b
=
15
. Find the response of the muscle when
x
=
30
.
Determine the value of
b
if
R
(
50
)
=
30
; that is, if a concentration of
x
=
50
units produces a
30
%
response.
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