3. The score of a test given as a percentage is given by S(t) = 50+ 14ln(t + 1), where t s equal to the number of hours a student studied for the test. How many hours should a student study in order to get a score of 90%?
3. The score of a test given as a percentage is given by S(t) = 50+ 14ln(t + 1), where t s equal to the number of hours a student studied for the test. How many hours should a student study in order to get a score of 90%?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Studies for the test
![**Problem 13:**
The score of a test given as a percentage is represented by the function \( S(t) = 50 + 14 \ln(t + 1) \), where \( t \) is the number of hours a student studied for the test. The question asks: How many hours should a student study in order to achieve a score of 90%?
To solve this, set \( S(t) = 90 \) and solve for \( t \).
1. Start with the equation:
\[ 90 = 50 + 14 \ln(t + 1) \]
2. Subtract 50 from both sides:
\[ 40 = 14 \ln(t + 1) \]
3. Divide both sides by 14:
\[ \ln(t + 1) = \frac{40}{14} \]
4. Simplify:
\[ \ln(t + 1) = \frac{20}{7} \]
5. Exponentiate both sides to remove the logarithm:
\[ t + 1 = e^{\frac{20}{7}} \]
6. Solve for \( t \):
\[ t = e^{\frac{20}{7}} - 1 \]
After calculating \( e^{\frac{20}{7}} \), the result gives the number of hours required for a student to study to achieve a 90% score.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87cce205-f851-4976-8397-03357e1ce3c0%2F0a1d3d6d-24ff-49d3-913c-d5e7ac1883d1%2F5cqr7eu5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 13:**
The score of a test given as a percentage is represented by the function \( S(t) = 50 + 14 \ln(t + 1) \), where \( t \) is the number of hours a student studied for the test. The question asks: How many hours should a student study in order to achieve a score of 90%?
To solve this, set \( S(t) = 90 \) and solve for \( t \).
1. Start with the equation:
\[ 90 = 50 + 14 \ln(t + 1) \]
2. Subtract 50 from both sides:
\[ 40 = 14 \ln(t + 1) \]
3. Divide both sides by 14:
\[ \ln(t + 1) = \frac{40}{14} \]
4. Simplify:
\[ \ln(t + 1) = \frac{20}{7} \]
5. Exponentiate both sides to remove the logarithm:
\[ t + 1 = e^{\frac{20}{7}} \]
6. Solve for \( t \):
\[ t = e^{\frac{20}{7}} - 1 \]
After calculating \( e^{\frac{20}{7}} \), the result gives the number of hours required for a student to study to achieve a 90% score.
Expert Solution
Step 1
given
s(t)=50+14ln(t+1)
here
s(t)=score of test as a percentage
t=hours a student studied for the test
Step by step
Solved in 2 steps
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