In a city, a rumour is spreading about the safety of corona vaccination. Suppose  N  number of people live in the city and  f ( t )  is the number of people who have not yet heard about the rumour after  t  days. Suppose  f ( t )  is given by  f ( t ) = N e − k t , where k is a constant. If the population of the city is  1000 , and suppose  40  have heard the rumor after the first day. After how many days (approximately) half of the population would have heard the rumor?

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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.