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Sagot :
The half-life of the substance is 3.106 years.
What is the formula for exponential decay?
- 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 = [tex]a_{0}[/tex]×[tex](0.8)^{t}[/tex]
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
Substituting this into the equation:
0.5[tex]a_{0}[/tex] = [tex]a_{0}[/tex]×[tex](0.8)^{t}[/tex]
0.5 = [tex](0.8)^{t}[/tex]
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.
To learn more about exponential decay formula visit:
https://brainly.com/question/28172854
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