Question

A substance decays so that the amount a of the substance left after t years is given by: a = a0 • (0.7)t, where a0 is the original amount of the substance. what is the half-life (the amount of time that it takes to decay to half the original amount) of this substance, rounded to the nearest tenth of a year?

Answer 1

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 $(1-r)^{x}$ 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:

$a=a_{0}$×$(0.7)^{t}$

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 $a_{0}=a_{0}$×$(0.7)^{t}$

0.5 = $(0.7)^{t}$

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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