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A kitten weighs 85 grams at birth. During the first four weeks after the kitten's birth, its weight in grams is given by the function w that satisfies the differential equation dw /dt =kw, where t is measured in days and k is some positive constant. Which of the following could be an expression for w(t)?
A kitten weighs 85 grams at birth. During the first four weeks after the kitten's birth, its weight in grams is given by the function w that satisfies the differential equation dw /dt =kw, where t is measured in days and k is some positive constant. Which of the following could be an expression for w(t)?a) w(t)=85eᵏᵗ
b) w(t)=85+kt
c) w(t)=85−kt
d) w(t)=85⋅kᵗ
The correct expression for the weight w(t) of a kitten that grows according to the given exponential model is w(t) = 85e^kt, which is option (a). It is the only option describing exponential growth as per the differential equation dw/dt = kw.The student's question is about finding the expression for the weight w(t) of a kitten that grows following the exponential growth model, with the differential equation dw/dt = kw. Given that the kitten weighs 85 grams at birth and t is measured in days, we look for a function that represents this growth. Since the growth is exponential, the function has the form of w(t) = 85ekt, where k is a constant growth rate, and e is the base of the natural logarithm.Option (a) w(t) = 85ekt is the only choice that reflects exponential growth consistent with the given differential equation. Therefore, the correct expression for w(t) is option (a)....