Question

The exponential formula for the half-life of a radioactive isotope is y=y0e^kt, where y is the amount of the isotope remaining after t years, y0 is the initial amount of the isotope, k is the decay constant, and e is the transcendental number approximately equal to 2.71828. How can you rearrange the given formula to correctly find y0? Possible answers below
y0=ye^kt
y0=y+e^kt
y0=y/e^kt
y0=y-3^kt

Answer 1

The formula of $y_{0}$ is: $y_{0}=\frac{y}{e^{kt}}$ ⇒ 3rd answer

Step-by-step explanation:

The exponential formula for the half-life of a radioactive isotope is

• $y=y_{0}e^{kt}$ , where
• y is the amount of the isotope remaining after t years
• $y_{0}$ is the initial amount of the isotope
• k is the decay constant
• e is the transcendental number approximately equal to 2.71828

We need to rearrange the given formula to find $y_{0}$

∵ $y=y_{0}e^{kt}$

- Divide both sides by $e^{kt}$

∴ $\frac{y}{e^{kt}}=\frac{y_{0}e^{kt}}{e^{kt}}$

∴ $\frac{y}{e^{kt}}={y_{0}$

The formula of $y_{0}$ is: $y_{0}=\frac{y}{e^{kt}}$

Learn more:

You can learn more about the exponent in brainly.com/question/13174260

#LearnwithBrainly