Which of the following terms best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity? A. Exponential decay B. Positive slope C. Negative slope D. Exponential growth

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Question

Which of the following terms best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity? A. Exponential decay B. Positive slope C. Negative slope D. Exponential growth

Answer 1

To solve this problem, let's consider the definitions of each term:A. **Exponential decay** refers to a process where a quantity decreases over time at a rate proportional to its current value. This is typically represented by a mathematical model where the quantity decreases by a constant percentage over equal time intervals. The formula for exponential decay is often written as $N(t) = N_0 \cdot e^{-kt}$, where $N(t)$ is the quantity at time $t$, $N_0$ is the initial quantity, $e$ is the base of the natural logarithm, and $k$ is the decay constant.B. **Positive slope** refers to a line on a graph that moves upward as it goes from left to right. This indicates that as the independent variable increases, the dependent variable also increases. It is not related to a rate that is proportional to the current value of a quantity.C. **Negative slope** refers to a line on a graph that moves downward as it goes from left to right. This indicates that as the independent variable increases, the dependent variable decreases. However, a negative slope does not necessarily mean that the rate of decrease is proportional to the current value of the quantity.D. **Exponential growth** is the opposite of exponential decay. It refers to a process where a quantity increases over time at a rate proportional to its current value. The formula for exponential growth is similar to decay but without the negative sign in the exponent: $N(t) = N_0 \cdot e^{kt}$.Given these definitions, the term that best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity is **A. Exponential decay**. This is because exponential decay specifically involves a rate of change that is proportional to the quantity's current value.**The accurate answer is A. Exponential decay.**

Question

Which of the following terms best describes a condition in which a quantity decreases at a rate that is proportional to the current value of the quantity? A. Exponential decay B. Positive slope C. Negative slope D. Exponential growth

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