exponential的音標是[?eksp??n???(?)l]，基本翻譯是“指數的；冪的；指數增長的”，速記技巧是：exponent-exp，-ial形容詞后綴。

Exponential這個詞源自拉丁語，意為“指數的”或“指數函數的”。它的變化形式包括名詞exponent（指數）和exponential（指數的），形容詞exponential（指數的）和動詞exponentialize（使指數化）。

相關單詞：

1. Exponential growth（指數增長）: 描述一個事物以指數形式快速增加，比如人口、網絡流量等。

2. Exponential decay（指數衰減）: 描述一個事物以指數形式逐漸減少，比如放射性物質的衰變。

3. Exponential function（指數函數）: 描述一個變量隨另一個變量指數變化的函數。

4. Exponential rate（指數率）: 描述一個變量隨時間或空間變化的速率，通常用指數函數來表達。

5. Exponential map（指數映射）: 在數學中，指數映射是一種特殊的映射，它把輸入映射到輸入的某個特定次冪。

6. Exponentiation（乘方）: 乘方運算就是指數為1的乘法運算，也就是指數函數的逆運算。

7. Exponential growth rate（增長率）: 描述一個系統或過程在一段時間內增長的速度，通常用指數增長來描述。

8. Exponential decay rate（衰減率）: 描述一個衰減過程的速度，通常用指數衰減來描述。

9. Exponential expansion（指數擴張）: 描述一個系統或物體以指數形式擴張或增長的過程。

10. Exponential decay rate in radioactivity（放射性物質的指數衰減速率）: 描述放射性物質衰變過程中衰減速度的術語。

常用短語：

1. exponential growth 指數增長

2. exponential decay 指數衰減

3. exponential function 指數函數

4. exponential rate 指數率

5. base-exponential equation 基指數方程

6. power law exponential 冪率指數函數

7. exponential rate of change 指數變化率

例句：

1. The number of online users is growing exponentially, leading to a surge in demand for bandwidth.

2. The decay of radioactive substances follows an exponential curve.

3. The graph of an exponential function looks like a stretched line.

4. The rate of inflation is expected to increase exponentially in the coming years.

5. The base-exponential equation y = exx is used in physics and engineering to model certain phenomena.

6. The exponential rate of change in the price of oil has a significant impact on the global economy.

英文小作文：

Exponential Change: The Future Is Unpredictable

In today"s fast-paced world, exponential change is a constant presence, shaping our lives in ways we cannot predict or prepare for. From technology to environmental issues, exponential growth and decay are affecting every aspect of our world, making the future an unpredictable and exciting place to be.

Take the field of artificial intelligence, for example. With each passing day, we see new breakthroughs in machine learning and AI, leading to exponential progress in areas such as speech recognition, image recognition, and natural language processing. These advances have the potential to revolutionize many industries, from healthcare to transportation to education.

Similarly, the field of climate science is facing an exponential rise in environmental issues such as climate change and pollution. With each passing year, we see more evidence of the impact of human activity on the planet"s ecosystems, leading to concerns about our future and the need for urgent action.

Exponential change can be both a challenge and an opportunity. It requires us to be adaptable and willing to embrace change, while also being aware of the impact we are having on our environment and on others. With proper planning and foresight, we can embrace this change and use it as an opportunity to create a better future for ourselves and for future generations.