Question

Find the initial amount in the sample and the amount remaining after 30 hours. Round your answers to the nearest gram as necessary.A(t) = 5600 * (1/2) ^ (t/14)The radioactive substance 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 bythe following exponential function.

Answer 1

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:

`A(t)=5600*((1)/(2))^{(t)/(14)}`

To know:

Find the initial amount in the sample and the amount remaining after 30 hours.

Step-by-step 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

`\begin{gathered} A(t)=5600((1)/(2))^{(t)/(14)} \\ A(0)=5600*1 \\ A(0)=5600 \end{gathered}`

And at t = 30 hours

`\begin{gathered} A(30)=5600*((1)/(2))^{(30)/(14)} \\ =1267.89 \end{gathered}`

Hence, 1267.89 gram is the answer.