A lush forest has 100 foxes and 2 rabbits. The fox population doubles every year and the rabbit population triples every year. The foxes agree not to hunt the rabbits until they are outnumbered by the rabbits. -Let t be the number of years that pass, and come up with two exponential expressions that model the fox population and rabbit population respectively. -The rabbits will equal (and then shortly outnumber) the foxes midway through some year. Find the value of t such that the two populations are equal, accurate to four decimal places, and the populations of each animal at that time to the nearest whole number.

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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.