A common inhabitant of human intestines is the bacteriumEscherichia coli. A cell of this bacterium in a nutrient-brothmedium divides into two cells every 20 minutes. The initialpopulation of a culture is 60 cells.(a) Find the relative growth rate.(b) Find an expression for the number of cells after hours.(c) Find the number of cells after 8 hours.(d) Find the rate of growth after 8 hours.(e) When will the population reach 20,000 cells?

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Q: 6. How is the instantaneous rate of change found?

A: Answer and explanation is given below..

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Q: How are the rate constant and the doubling time related?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.