Let T Represent the Number of Hours That a Packing $y ^ { \prime }$

question 1

Multiple Choice

Let t represent the number of hours that a packing machine is operated and y(t) represent the probability that the machine breaks down at least once during the t hours of operation. It has been observed that the rate of increase of the probability of a breakdown is proportional to the probability of not having a breakdown. Find a differential equation describing this situation.

• A) \(y ^ { \prime }\) = ky; There is not enough information given to determine initial conditions.
• B) \(y ^ { \prime }\) = ky; y(0) = 0
• C) \(y ^ { \prime }\) = k(1 - y); There is not enough information given to determine initial conditions.
• D) \(y ^ { \prime }\) = k(1 - y); y(0) = 0
• E) \(y ^ { \prime }\) = (1 + y); y(0) =0

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Definitions:

Biological Processes

Complex sequences of actions or changes happening in living organisms, necessary for their survival, growth, and reproduction.

Ionic Bond

A chemical bond formed between two atoms when one atom transfers an electron to another, leading to the attraction between positively and negatively charged ions.

Hydrogen Bond

An insubstantial attachment between two molecules produced by the electrostatic allure between a proton of one molecule and an electronegative atom of the other.

Ions

Atoms or molecules that have lost or gained one or more electrons, thus acquiring an electric charge.