Step-by-step explanation:
To solve this, we can use the radioactive decay formula:
\[ N(t) = N_0 \times (0.5)^{\frac{t}{T_{\text{half}}}} \]
Where:
- \( N(t) \) is the amount of radioactive substance at time \( t \)
- \( N_0 \) is the initial amount of the substance
- \( T_{\text{half}} \) is the half-life of the substance
Given:
- \( N_0 = 3.75 \) ml
- \( T_{\text{half}} = 1.9 \) hours
We want to find \( t \) when \( N(t) = 0.36 \) ml.
\[ 0.36 = 3.75 \times (0.5)^{\frac{t}{1.9}} \]
Now, solve for \( t \):
\[ \frac{0.36}{3.75} = (0.5)^{\frac{t}{1.9}} \]
\[ \frac{0.36}{3.75} = (0.5)^{\frac{t}{1.9}} \]
\[ \log_{0.5}\left(\frac{0.36}{3.75}\right) = \frac{t}{1.9} \]
\[ t = 1.9 \times \log_{0.5}\left(\frac{0.36}{3.75}\right) \]
Calculate \( t \) using a calculator:
\[ t ≈ 5.85 \]
So, at approximately \( t ≈ 5.85 \) hours after 6:30 am, which is around 12:15 pm, the amount of liquid will decrease to 0.36 ml.
