Answer:
1.97 ounces
Step-by-step explanation:
-The exponential decay function is given by the formula:
[tex]P_t=P_oe^{-rt}\\\\[/tex]
Given that the half-life is 4 days, we can substitute in the formula to solve the rate of decay for a single half-life:
[tex]P_t=P_oe^{rt}\\\\P_t=0.5P_o\\\\\therefore 0.5=e^{-4r}\\\\-4r=In(0.5)\\\\r=0.17329[/tex]
#Since, 1 week has 7 days, 3 weeks is a 21-day period, thus, t=21.
#We substitute and solve for the amount remaining after 21days of decay:
[tex]P_t=P_oe^{-rt}\\\\=75e^{-21\times 0.17329}\\\\=1.97072\\\\\approx1.97 \ oz[/tex]
Hence, the amount remaining after 3 weeks of decays is approximately 1.97 ounces
