In an animal hospital, 10 units of a certain medicine were injected into a dog. After 40 minutes, only 5 units remained in the dog. Let f(t) be the amount of the medicine present after t minutes. At any time, the rate of change of f(t) is proportional to the value of f(t). Find the formula for f(t). The formula is f(t) = (Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.)
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We know that the rate of change of f(t) is proportional to the value of f(t). This can be represented as: df/dt = -kf(t) where k is a constant of proportionality and the negative sign indicates that the amount of medicine is decreasing over time. Show more…
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