50. Fungal Growth As a fungus grows, its rate of growth changes. Young fungi grow exponentially, while in larger fungi growth slows, and the total dimensions of the fungus increase as a linear function of time. You want to build a mathematical model that describes the two phases of growth. Specifically if R(f) is the rate of growth given as a function of time, t, then you model 2e if 0t < tc la if t > tc R(t) where te is the time at which the fungus switches from exponential to linear growth and a is a constant a. For what value of a is the function R(t) continuous at t te? (Your answer will include the unknown constant te) b. Assume that te = 2. Draw the graph of R(t) as a function of t

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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.