grows exponentially with

USAGE SUMMARY

The phrase "grows exponentially with" is a correct and usable phrase in written English.
You can use it to describe a situation where something increases in a rapid and powerful way. For example, "The amount of data stored on the internet grows exponentially with every new day."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The law says that the value of a network grows exponentially with the number of its users.

The New Yorker

Thus, the complexity grows exponentially with.

EURASIP Journal on Advances in Signal Processing

Also, the calendar aging grows exponentially with the temperature.

EURASIP Journal on Wireless Communications and Networking

This complexity grows exponentially with the number of transmitters.

EURASIP Journal on Wireless Communications and Networking

It grows exponentially with the sub-channel number [24].

EURASIP Journal on Advances in Signal Processing

The vulnerability of such systems to soft errors grows exponentially with technology scaling.

Microelectronics Reliability

To obtain accurate and reliable results, the amount of samples often grows exponentially with the dimensions.

Applied Soft Computing

The amount of bio-medical data available on the Web grows exponentially with time.

Web Semantics: Science, Services and Agents on the World Wide Web

The Internet grows exponentially with the proliferation of network devices, mobile terminals and users.

Security in Network Functions Virtualization

But the computational cost of classic PCE grows exponentially with the size of the input variables.

Computers & Structures

The number of possible paths grows exponentially with the number of celestial bodies.

Acta Astronautica

Expert writing Tips

Best practice

Use this phrase when you want to emphasize the rapid and accelerating nature of an increase. It's stronger than simply saying something 'increases' or 'grows quickly'.

Common error

Avoid using "grows exponentially with" when the growth is merely rapid or significant, but not truly exponential. Exponential growth has a specific mathematical definition; ensure the context aligns with this definition to avoid misleading your audience.

Linguistic Context

The phrase "grows exponentially with" functions as a verb phrase indicating the manner in which something increases in relation to another variable. As Ludwig AI points out, it describes a situation where one quantity increases at an accelerating rate as another increases.

Expression frequency: Very common

Frequent in

Science

85%

News & Media

7%

Formal & Business

5%

Less common in

Academia

1%

Encyclopedias

1%

Wiki

1%

Ludwig's WRAP-UP

In summary, the phrase "grows exponentially with" is a grammatically sound and frequently used expression, particularly within scientific and technical domains. As Ludwig AI confirms, it accurately portrays a relationship where one variable increases at an accelerating rate relative to another. The phrase serves to emphasize the rapid and accelerating nature of the increase, highlighting a strong dependency between two factors. When employing this phrase, it's important to ensure the context genuinely supports the claim of exponential growth, avoiding its misuse for mere rapid increases. Be also cautious not to overuse the phrase, diluting its power when truly exponential relationships need to be emphasized.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

grows at an exponential rate with

Emphasizes the rate of exponential growth.

exhibits exponential growth with

More explicitly mentions exponential growth as a characteristic.

increases rapidly with

Emphasizes the speed of the increase rather than the mathematical nature of exponential growth.

shows an exponential relationship with

Highlights the exponential nature of the relationship between two entities.

scales exponentially with

Focuses on the scaling aspect, suggesting a proportional exponential change.

amplifies exponentially with

Suggests an increasing amplification effect.

is directly proportional to the exponential of

More mathematically precise, highlighting the direct proportionality to an exponential function.

varies exponentially with

Indicates a relationship where changes are exponential but doesn't specify growth.

proliferates exponentially with

Highlights the rapid multiplication or spread of something.

is an exponential function of

States that one quantity is mathematically defined by the exponential of another.

FAQs

How do you use "grows exponentially with" in a sentence?

You can use "grows exponentially with" to describe a situation where something increases at an accelerating rate in relation to another factor. For example, "The computational complexity "grows exponentially with" the size of the input data".

What are some alternatives to "grows exponentially with"?

Alternatives include "increases rapidly with", "scales exponentially with", or "exhibits exponential growth with". The best choice depends on the specific nuance you want to convey.

Is it correct to say something "grows exponentially with time"?

Yes, it is correct. It means that the quantity in question increases at an accelerating rate as time passes. This is a common usage, particularly in scientific and technical contexts.

What's the difference between "grows linearly with" and "grows exponentially with"?

"Grows linearly with" means the increase is constant and proportional to the other variable, while "grows exponentially with" means the increase is accelerating; the rate of growth itself increases as the other variable increases. For example: "Sales increase linearly with marketing spend" vs. "Network value "grows exponentially with" user adoption".