The formula D=5 e^-0.4 h can be used to find the number of...

The formula $$D=5 e^{-0.4 h}$$ can be used to find the number of milligrams $D$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug was administered. When the number of milligrams reaches 2 the drug is to be administered again. What is the time between injections?

The formula
$$D=5 e^{-0.4 h}$$
can be used to find the number of milligrams $D$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug was administered. When the number of milligrams reaches 2 the drug is to be administered again. What is the time between injections?

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Key Concepts

Exponential Decay

Exponential decay refers to the process in which a quantity decreases at a rate proportional to its current value. This behavior is modeled by an equation of the form A = A?e^(–kt), where A? is the initial amount, k is the decay constant, and t is time. The concept is widely applicable in various fields such as physics, chemistry, and biology.

Natural Logarithms

Natural logarithms are the inverse functions of exponential functions with base e. They are used to unravel variables that appear as exponents in equations, transforming multiplicative relationships into additive ones and thereby simplifying the process of solving for the unknown.

Solving Exponential Equations

Solving exponential equations involves isolating the exponential term and then applying a logarithm to both sides of the equation. This step helps to extract the variable from the exponent, allowing for the determination of time or rate parameters in models of exponential growth or decay.

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