You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if its half-life is 5 days? square grams

## Step 1<br />The problem involves the concept of half-life in radioactive decay. The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of the radioactive bismuth is given as 5 days.<br /><br />## Step 2<br />The formula to calculate the remaining amount of a radioactive substance after a certain number of half-lives is:<br />### \(N = N_0 \times (1/2)^{\frac{t}{T}}\)<br />where:<br />- \(N\) is the remaining amount of the substance,<br />- \(N_0\) is the initial amount of the substance,<br />- \(t\) is the time elapsed,<br />- \(T\) is the half-life of the substance.<br /><br />## Step 3<br />In this problem, we are given:<br />- \(N_0 = 7160\) grams (the initial amount of bismuth),<br />- \(t = 10\) days (the time elapsed),<br />- \(T = 5\) days (the half-life of the bismuth).<br /><br />## Step 4<br />Substituting these values into the formula, we get:<br />### \(N = 7160 \times (1/2)^{\frac{10}{5}}\)<br /><br />## Step 5<br />Simplifying the above expression, we get:<br />### \(N = 7160 \times (1/2)^2\)<br /><br />## Step 6<br />Further simplifying, we get:<br />### \(N = 7160 \times 1/4\)<br /><br />## Step 7<br />Finally, we get:<br />### \(N = 1790\) grams