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.
Listen
A falling object travels a distance given by the formula d = 6t + 9t2 where d is in feet
and t is the time in seconds. How many seconds will it take for the object to travel
112 feet? Round answer to 2 decimal places. (Write the number, not the units).
Your Answer:
Solve by the quadratic formula or completing the square to obtain exact solutions.
2
e
104
OA) -16±3√6
B) 8±√10
O c) -8±√10
OD) 8±3√√6
U
Question 14 (1 point)
Listen
The frame on a picture is 18 in by 22 in outside and is of uniform width. Using
algebraic methods, what is the width of the frame if the inner area of the picture
shown is 250 in²2? Write answer to 2 decimal places. (Write the number with no
units).
18 in
Your Answer:
22 in
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