In(19/t+1) 4/t Minimum Level of Stabilization: 2.73125 Maximum Level of Stabilization: 3.740625 s(t): =

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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i need to know if the level of stableization goes to hig or to low

### Mathematical Formula and Its Application

The formula presented is used to determine the stabilization level over time, denoted as \( s(t) \).

#### Formula:
\[
s(t) = \frac{\ln(19/t+1)}{4/t}
\]

Where:
- \( s(t) \) is the stabilization level at time \( t \).
- \( \ln \) denotes the natural logarithm.
- \( 19/t+1 \) is the expression inside the logarithm.
- \( 4/t \) is the denominator, indicating a division by \( t \) scaled by 4.

#### Key Values:
- **Minimum Level of Stabilization:** 2.73125
- **Maximum Level of Stabilization:** 3.740625

These values represent the range within which the stabilization level varies over the observed timeframe.

#### Explanation:
This formula provides insights into how certain conditions stabilize over time, considering the logarithmic growth effect and the diminishing return as time increases. The use of the natural logarithm implies a relationship that rapidly increases before plateauing. The minimum and maximum values indicate the limits of this stabilization process under specified conditions.
Transcribed Image Text:### Mathematical Formula and Its Application The formula presented is used to determine the stabilization level over time, denoted as \( s(t) \). #### Formula: \[ s(t) = \frac{\ln(19/t+1)}{4/t} \] Where: - \( s(t) \) is the stabilization level at time \( t \). - \( \ln \) denotes the natural logarithm. - \( 19/t+1 \) is the expression inside the logarithm. - \( 4/t \) is the denominator, indicating a division by \( t \) scaled by 4. #### Key Values: - **Minimum Level of Stabilization:** 2.73125 - **Maximum Level of Stabilization:** 3.740625 These values represent the range within which the stabilization level varies over the observed timeframe. #### Explanation: This formula provides insights into how certain conditions stabilize over time, considering the logarithmic growth effect and the diminishing return as time increases. The use of the natural logarithm implies a relationship that rapidly increases before plateauing. The minimum and maximum values indicate the limits of this stabilization process under specified conditions.
Expert Solution
Step 1: The given data is:

straight s open parentheses straight t close parentheses equals fraction numerator ln open parentheses 19 over straight t plus 1 close parentheses over denominator 4 over straight t end fraction 

Minimum level of stabilization: 2.73125

Maximum level of stabilization: 3.740625

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