Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is P = 0.9 x − 0.4 0.9 x + 0.1 , where P is the proportion of correct responses after x trials If P = 0 , there are no correct responses If P = 1 , all responses are correct. The graph of the rational formula is shown. Use the formula to solve Exercises 103-104. How many learning trials are necessary for 0.5 of the responses to be correct? Identify your solution as a point on the graph.
Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is P = 0.9 x − 0.4 0.9 x + 0.1 , where P is the proportion of correct responses after x trials If P = 0 , there are no correct responses If P = 1 , all responses are correct. The graph of the rational formula is shown. Use the formula to solve Exercises 103-104. How many learning trials are necessary for 0.5 of the responses to be correct? Identify your solution as a point on the graph.
Solution Summary: The author calculates the number of learning trials which are necessary for 0.5 of the responses to be correct.
Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is
P
=
0.9
x
−
0.4
0.9
x
+
0.1
,
where P is the proportion of correct responses after x trials If
P
=
0
, there are no correct responses If
P
=
1
, all responses are correct. The graph of the rational formula is shown. Use the formula to solve Exercises 103-104.
How many learning trials are necessary for 0.5 of the responses to be correct? Identify your solution as a point on the graph.
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Determine if the values of the variables listed are solutions of the system of equations.
2x - y = 4
3x+5y= - 6
x=1, y = 2; (1,-2)
Is (1, 2) a solution of the system of equations?
L
No
Yes
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10. A sound wave's amplitude can be modeled by the function y = −7 sin ((x-1) + 4). Within the interval 0 < x < 12, when does the function have an amplitude
of 4? (Select all that apply.)
9.522 seconds
4.199 seconds
0.522 seconds
1.199 seconds
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