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I heard people say that the exponential to the power of R times T

e^{rt}

Is it normal?

What about other similar things?

e^{-rt}

Is it read

the exponential to the negative power of R times T

or

the exponential to the power of negative R times T

or

the exponential to the negative exponent of R times T

What do you think about?

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    $\begingroup$ sometimes I say, "e to the (negative) r t" $\endgroup$ Jan 14, 2021 at 1:48
  • $\begingroup$ For the other situation, do you say "e to the negative r t"? thx $\endgroup$ Jan 14, 2021 at 1:50
  • $\begingroup$ How about "the exponential to the negative r t"? $\endgroup$ Jan 14, 2021 at 1:52
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    $\begingroup$ I think it doesn't matter but I say $e^M$ as "e to the M" whatever M is, so I'd so $e^{-rt}$ as "eee to the negative arrh tee" ... anyway "the exponential to the negative exponent of R times T" doesn't really make any sense. $\endgroup$
    – fleablood
    Jan 14, 2021 at 1:53
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    $\begingroup$ No, it is not clear. "The exponential" isn't a thing. "Exponential" is an adjective; you need a noun. There are exponential distributions. There is an exponential function, but the function is not being raised to a power. $\endgroup$
    – David K
    Jan 14, 2021 at 3:37

1 Answer 1

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The expression e^rt is sloppy. Either write it as $e^{rt}$ or e^{rt} so that you won't confuse it with $e^r\cdot t$. (The expression $\exp(rt)$ is also used very often.)

As long as the context is clear, "$e$ to the power of $rt$" is a usual way to read it.

Similarly, I would write e^{-rt} or $e^{-rt}$ to avoid any confusion. "$e$ to the power of negative $rt$" is reasonable.

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  • $\begingroup$ Yes. For beginners, or non-experts, include the word "power" in there. As a short-cut, leave it out. $\endgroup$
    – GEdgar
    Jan 14, 2021 at 2:23

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