The half-life of the substance is 3.106 years.
<h3>What is the formula for exponential decay?</h3>- The exponential decline, which is a rapid reduction over time, can be calculated with the use of the exponential decay formula.
- The exponential decay formula is used to determine population decay, half-life, radioactivity decay, and other phenomena.
- The general form is F(x) = a.
Here,
a = the initial amount of substance
1-r is the decay rate
x = time span
The equation is given in its correct form as follows:
a = ×
As this is an exponential decay of a first order reaction, t is an exponent of 0.8.
Now let's figure out the half life. Since the amount left is half of the initial amount at time t, that is when:
a = 0.5 a0
<h3>Substituting this into the equation:</h3>0.5 =
×
0.5 =
taking log on both sides
t log 0.8 = log 0.5
t = log 0.5/log 0.8
t = 3.106 years
The half-life of the substance is 3.106 years.
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