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Sagot :
The half-life of the substance is 1.94 years.
What is exponential decay formula?
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a [tex](1-r)^{x}[/tex] is the general form.
Here
a = the initial amount of substance
1-r is the decay rate
x = time span
The correct form of the equation is given as:
[tex]a=a_{0}[/tex]×[tex](0.7)^{t}[/tex]
where t is an exponent of 0.7 since this is an exponential decay of 1st order reaction
Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:
a = 0.5 a0
Substituting this into the equation:
0.5 [tex]a_{0}=a_{0}[/tex]×[tex](0.7)^{t}[/tex]
0.5 = [tex](0.7)^{t}[/tex]
Taking the log of both sides:
t log 0.7 = log 0.5
t = log 0.5 / log 0.7
t = 1.94 years
The half life of the substance is 1.94 years.
To learn more about exponential decay formula, visit: https://brainly.com/question/13615320
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