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Answer :
The constant 0.9975 represents an exponential decay in the quantity, indicating that the quantity decreases by a certain percentage every month.
The constant 0.9975 in the function f(t) = 190 Times (0.9975){ rac{t}{30}} reveals about the rate of change of the quantity that it is decreasing over time. Since the constant is less than 1, it indicates that the quantity is subject to exponential decay.
The function models this decay process, where every month, the quantity multiplies by 0.9975 raised to the power of the fraction of 30 (t/30), signifying a gradual decrease. This type of function is often solved using the principles of differential equations, where the derivative of the quantity Q(t) is proportional to Q(t) itself, implying that the function is an exponentially changing one. For instance, if we had a velocity function v(t), its derivative would represent acceleration, indicating the rate at which velocity changes over time.
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