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Amiraneli [1.4K]
3 years ago
15

A certain compound has a half-life of four days. Write and use an exponential decay function to find the amount of compound rema

ining from a 75-ounce sample after three weeks .
Mathematics
1 answer:
dimaraw [331]3 years ago
4 0

Answer:

1.97 ounces

Step-by-step explanation:

-The exponential decay function is given by the formula:

P_t=P_oe^{-rt}\\\\

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:

P_t=P_oe^{rt}\\\\P_t=0.5P_o\\\\\therefore 0.5=e^{-4r}\\\\-4r=In(0.5)\\\\r=0.17329

#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:

P_t=P_oe^{-rt}\\\\=75e^{-21\times 0.17329}\\\\=1.97072\\\\\approx1.97 \ oz

Hence, the amount remaining after 3 weeks of decays is approximately 1.97 ounces

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Step-by-step explanation:

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Step 5: This gives us a pair of simple equations:

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Step 7: Taking the inverse (or reciprocal) of both sides yields

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