Which of the Following Functions Y = F(x) Satisfy Y'= $\frac { 1 } { 2 }$

question 61

Multiple Choice

Which of the following functions y = f(x) satisfy y'= 32y, f (0) = $\frac { 1 } { 2 }$ ?
(I) y = 32 $e ^ { 1 / 2 x }$
(II) y = $\mathrm { e } ^ { 16 x }$
(III) y = $\frac { 1 } { 2 }$ $e ^ { 32 x }$ (IV) y = $\frac { 1 } { 2 }$ $x ^ { 32 }$

• A) I only
• B) IV only
• C) III only
• D) I and II
• E) none of these

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Definitions:

Nonzero Differences

Differences between values or measurements that are not equal to zero, indicating variation or change.

Matched-Pairs Sampling

A method of sampling that involves pairing each subject with another subject that is similar in terms of key variables, then treating one with the experiment and the other with the control condition.

Wilcoxon Signed-Rank Test

A non-parametric statistical test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ.

Paired-Difference Experiment

A study design where the subjects are paired up based on certain criteria, and differences within each pair are studied.