Solve the Problem by Integration $t$ (In Min) Required to Form $x$

question 190

Multiple Choice

Solve the problem by integration.
-Under specified conditions, the time $t$ (in min) required to form $x$ grams of a substance during a chemical reaction is given by $t = \int \frac { d x } { ( 7 - x ) ( 2 - x ) }$ . Find the equation relating $t$ and $x$ if $x = 0 g$ when $t = 0$ min.

• A) \(t = \frac { 1 } { 5 } \ln \left| \frac { 2 - x } { 7 - x } \right| - \frac { 1 } { 5 } \ln \frac { 2 } { 7 }\)
• B) \(t = \frac { 1 } { 5 } \ln \left| \frac { 7 - x } { 2 - x } \right| + \frac { 1 } { 5 } \ln \frac { 7 } { 2 }\)
• C) \(t = \frac { 1 } { 5 } \ln \left| \frac { 7 - x } { 2 - x } \right| - \frac { 1 } { 5 } \ln \frac { 7 } { 2 }\)
• D) \(t = \frac { 1 } { 5 } \ln \left| \frac { 2 - x } { 7 - x } \right| + \frac { 1 } { 5 } \ln \frac { 2 } { 7 }\)

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Definitions:

Chromosome 11

One of the 23 pairs of chromosomes in humans, containing genes important for immune function, cell cycle regulation, and various metabolic processes.

Mutation

Change in the number or kinds of nucleotides in the DNA of a gene.

Leukocytes

White blood cells that are part of the immune system, defending the body against infection and disease.

Formed Elements

The cells and cell fragments in the blood, such as red blood cells, white blood cells, and platelets, that are critical for blood clotting, oxygen transport, and immune defense.