exponentially

Thân thiện

Inflation is growing exponentially, as shown by a steeply rising curve on a chart.

Definition

1. Adverb:
   • In an exponential manner: Increasing or decreasing at a rate proportional to the current value, resulting in a very rapid, accelerating change. This describes a pattern of growth or decay where the rate of change itself increases (or decreases) over time.

Usage

The adverb "exponentially" is used to describe a process of change that is not linear or steady, but instead becomes progressively faster or slower. It is most commonly applied to growth, but can also describe decay. - It modifies verbs, particularly those describing change (e.g., grow, increase, rise, decrease, decline). - It is often used in mathematical, scientific, technological, and business contexts to describe rapid, accelerating trends.

Examples

• General Usage:
  • The computing power of devices has increased exponentially over the last two decades.
  • Interest in the new product grew exponentially after the influencer's review.
  • Without intervention, the invasive species population can expand exponentially.

Advanced Usage

• "to grow exponentially": This is the most frequent collocation, emphasizing an accelerating rate of increase.
  • The data from the experiment shows the bacteria colony grew exponentially under ideal conditions.
• "to increase exponentially": Synonymous with "grow exponentially," often used with measurable quantities.
  • Demand for the service has increased exponentially.
• "exponentially faster/slower": Used to compare rates of change.
  • This new algorithm processes information exponentially faster than the old one.

Variants and Related Words

• Exponential (adjective): Of or relating to an exponent or exponential function. Characterized by or being an extremely rapid increase.
  • The company is on an exponential growth trajectory.
  • We observed an exponential curve in the data.
• Exponent (noun): A mathematical symbol (e.g., the 3 in 2³) or a person who advocates for something.
  • In the equation y = x², the exponent is 2.

Synonyms

• Rapidly: At a fast speed. (Less specific than exponentially, does not imply acceleration.)
• Dramatically: In a striking and noticeable way.
• Steeply: Rising or falling sharply. (Often used for linear graphs with a high slope.)

Antonyms

• Linearly: In a straight-line or proportional manner, at a constant rate.
• Gradually: Taking place slowly over time.
• Incrementally: In small, discrete steps or amounts.

Common Phrases and Collocations

• Exponential growth/decay: The specific mathematical and conceptual models of accelerating increase or decrease.
  • The textbook chapter explains the concept of exponential decay in radioactive materials.
• Rise exponentially: To increase at an accelerating rate.
  • Healthcare costs continue to rise exponentially in many countries.

Học thuật

Adverb

1. in an exponential manner
   • inflation is growing exponentially