16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T500,{"@context":"https://schema.org","@type":"Quiz","name":"Mht Cet 2020 Differential Equations PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/mht-cet/questions/2020/mathematics/differential-equations/luascw2o","educationalLevel":"Entrance exam preparation","about":"Mht Cet / Mathematics / Differential Equations","hasPart":{"@type":"Question","name":"Mht Cet 2020 Differential Equations PYQ with Solution","text":"The bacteria increases at the rate proportional to the number of bacteria present. If the original number 'N' doubles in 4 \\mathrm{~h}, then the number of bacteria in 12 \\mathrm{~h} will be","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"B"},"comment":{"@type":"Comment","text":"The given problem describes a classic case of exponential growth, which can be modeled with the equation: N(t) = N_0 \\cdot e^{kt} where: N(t) is the number of bacteria at time t, N_0 is the initial number of bacteria (here represented as N), k is the rate constant, and t is the time in hours. It's given that the number of bacteria doubles in 4 hours. This means that N(4) = 2N_0 (or simply, 2N if we denote N_0 as N). We can use this information to solve for k: 2N = N \\cdot e^{4k} By simplifying,..."}}}18:T4de,

The given problem describes a classic case of exponential growth, which can be modeled with the equation:

$$N(t) = N_0 \cdot e^{kt}$$

where:

$$N(t)$$ is the number of bacteria at time $$t$$,
$$N_0$$ is the initial nu

Differential Equations

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