Question

a 25 gram sample of a substance that's used for drug research has a k-value of 0.1205
Find the substance half life, in days. Round your answer to the nearest tenth

Answer 1

$$\Large{
A(t) =A_o e^{kt}
\\~\\
A(t) = 25 e^{0.1205 t }
}
$$

Answer 2

A(t) is the amount at t days, and Ao is the initial amount

Answer 3

now you want to find the half-life, which is the time it takes to get half the initial amount . so you need to solve
$$\Large{

25/2 = 25 e^{0.1205 t }
}
$$

Answer 4

How do I enter an e into the calculator?

Answer 5

5=25e^0.1205t?

Answer 6

@perl

Answer 7

-0.693= 0.1205 ?

Answer 8

ok k should be negative, since we doing radioactive decay

Answer 9

$$\Large{

\frac{25}{2} = 25 e^{-0.1205 t }
}
$$divide both sides by 25
$$\Large{

\frac{1}{2} = e^{-0.1205 t }
}
$$now take ln of both sides
$$
\Large{
\ln\left(\frac{1}{2}\right) = \ln (e^{-0.1205 t })
}
$$use properties of logs, we can bring down exponent
$$
\Large{
\ln\left(\frac{1}{2}\right) = -0.1205 t \cdot \ln (e)
}
$$ ln(e) = 1
$$
\Large{
\ln\left(\frac{1}{2}\right) = -0.1205 t \cdot 1
\\ \frac{\ln\left(\frac{1}{2}\right)}{-0.1205} = t


}
$$