a. Explanation The growth rate of culture of bacteria is proportional to the number of bacteria present and after 1 day is 1.25 times the original number. The population of bacteria at time t is, y ( t ) . Let k be the proportionality constant. Hence, the given statement can be modeled by the ODE, y ′ ( t ) = k y . Rewrite the ODE as, d y y = k d t . Integrate and find the solution of d y y = k d t as follows. ∫ d y y = ∫ k d t ln | y | = k t + C y = e k t + C y = c e k t ( ∵ e C = c ) Consider there are y ( 0 ) = y 0 bacteria at present. Applying the initial condition y ( 0 ) = y 0 in y = c e k t yields y = y 0 e k t b. To determine The time interval in which the number of bacteria will get triple?

10th Edition

ISBN: 9781119455929

Author: Kreyszig

Publisher: WILEY

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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 differentia…

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Chapter 1, Problem 27RQ

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The time interval in which the number of bacteria will get double?

To determine

The time interval in which the number of bacteria will get triple?

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