Problema Solution
Find the half-life of a radioactive substance that decays from 80mg to 15mg in 25 years according to the exponential decay model y=ae^bx,where a is the initial amount and y is the amount remaining after x years.
HINT: Find the b -value, then use this value to write the exponential model for this substance with the initial amount 80 mg.
If the answer is not an integer, enter it as a decimal rounded to the nearest tenth of a year if needed.
Note:"e" is that special number 2.718
Answer provided by our tutors
a = 80 mg
y = 15 mg
x = 25
y = ae^(bx)
80*e^(25b) = 15
e^(25b) = 15/80
25b = ln(15/80)
b = (1/25) (ln(15/80))
b = -0.1
click here to see the step by step solution of the equation
the exponential model for this substance with the initial amount 80 mg is:
y = 80*e^(-0.1t)