3) A researcher has collected population data along with time. Afler comparing the populations from consecutive times, he finds out the population is increasing and also that in the early slages, the rate of change of the population (derivalive with respeet to time) is proportional to the population itsclf. aj Find an equation describing this situation. What can you say regarding the coefficient of proportionality (positive or negative)? Explain. bi The rescarcher decides to make a corrcction to this cquation by subtracting a constant (the rate of change of the population with respect to time becomes proportional to the population itsclf minus a constant). Give an expression for the general solution of this HOuntion

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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.