Question

A certain compound has a half-life of four days. Write and use an exponential decay function to find the amount of compound remaining from a 75-ounce sample after three weeks .

Answer 1

1.97 ounces

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* 0.17329)\\\\=1.97072\\\\\approx1.97 \ oz`

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