If E and E_0 represent the energies, and t an | vedclass

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(D) For an equation to be dimensionally correct, the exponent of an exponential function must be dimensionless. In the expression $E=E_0 e^{-t / t_0}$

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$E=E_0 e^{-t / t_0}$

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(D) For an equation to be dimensionally correct, the exponent of an exponential function must be dimensionless. In the expression $E=E_0 e^{-t / t_0}$, the term $-t / t_0$ is the ratio of two times, which is dimensionless. Since $E$ and $E_0$ both represent energy, they have the same dimensional formula $[M L^2 T^{-2}]$. Therefore, the equation $E=E_0 e^{-t / t_0}$ is dimensionally consistent because the exponential factor $e^{-t / t_0}$ is a dimensionless constant. Other options are dimensionally incorrect because their exponents are not dimensionless or the dimensions on both sides do not match.

If $E$ and $E_0$ represent the energies, and $t$ and $t_0$ represent the times, which of the following relations is dimensionally correct?

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