Given:
The radioactive substances uranium-240 has a half-life of 14 hours. The amount A(t) of a sample of uranium-240 remaining (in grams ) after t hours is given by the following exponential function:
[tex]A(t)=5600\times(\frac{1}{2})^{\frac{t}{14}}[/tex]
To know:
Find the initial amount in the sample and the amount remaining after 30 hours.
Explanation:
Initial amount will be at t =0 and at t = ti time.
Solution:
We will take function A(t), at t=0 initial amount
[tex]\begin{gathered} A(t)=5600(\frac{1}{2})^{\frac{t}{14}} \\ A(0)=5600\times1 \\ A(0)=5600 \end{gathered}[/tex]
And at t = 30 hours
[tex]\begin{gathered} A(30)=5600\times(\frac{1}{2})^{\frac{30}{14}} \\ =1267.89 \end{gathered}[/tex]
Hence, 1267.89 gram is the answer.
