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asmita9876
30.06.2020 •
Mathematics
The rate at which a certain radioactive isotope decays is given by = negative 0.0032 y, where y is the amount of the isotope after t days. After approximately how many days would the amount of this isotope in a sample reach 75% of its original amount?
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Ответ:
90 days.
Step-by-step explanation:
dy/dt = - 0.0032y
dy = -0.0032y dt
dy/y = -0.0032 dt
Integrating:
ln y = -0.0032t + c where c is some constant
y = e^(-0032t) + e^c
y = A e^(-0032t) where A is a constant.
At time 0 we can let y = 1 so in that case A = 1
When there is 0.75 of y left:
0.75 = e^-0032t
ln 0,75 = -0032 t
t = ln 0.75 / -0032
t = 90.
Ответ:
1.24
Step-by-step explanation: