Texexp-314 is an isotope that is decaying \( 17 \% \) each day. Chemists initially have a 289-gram sample. Which of the following equations represents the amount of the isotope remaining after \( d \) days? \( y=289(0.17)^{d} \) \( y=289(0.83)^{d} \) \( y=289(1.17)^{d} \) \( y=314(0.83)^{d} \)

To determine the correct equation, we need to understand the decay process. Since Texexp-314 is decaying \( 17\% \) each day, that means \( 83\% \) of the sample remains after each day. Thus, we can represent the remaining amount using the formula: initial amount multiplied by the remaining percentage raised to the power of the number of days. The correct equation is \( y = 289(0.83)^{d} \), as it accurately reflects that \( 83\% \) of the isotope remains after each day. The concept of exponential decay can be seen in various natural processes, such as radioactive decay and the cooling of warm objects. Interestingly, just like a decaying isotope, our smartphone batteries also lose charge over time, demonstrating the science of decay in everyday life. So, next time you check your battery percentage or reminisce about a half-forgotten snack, remember—you’ve got a little science in your pocket!