Julie has 250 grams of a radioactive substance. The substance decays every hour. How long will it take until she has 20 grams of the substance left?

20

To determine how long it will take for Julie to have 20 grams of the radioactive substance left, we need to understand the concept of radioactive decay and use the half-life equation.

The half-life of a substance is the time it takes for half of the original amount to decay. The radioactive decay can be modeled by an exponential decay function.

In this case, we don't have the specific half-life of the substance, so we will need to calculate it.

Let's assume the half-life of the substance is 't' hours.

According to the half-life equation, the amount of the substance remaining after 't' hours can be calculated using the formula:

Amount remaining = Initial amount * (1/2)^(t/half-life)

We are given that Julie has 250 grams of the substance initially and wants to know when she will have 20 grams left. So, we can set up the equation:

20 = 250 * (1/2)^(t/half-life)

To solve for 't/half-life', we can take the natural logarithm of both sides of the equation:

ln(20) = ln(250) + (t/half-life) * ln(1/2)

Now, we know the values of the initial amount (250 grams), the amount remaining (20 grams), and we can also calculate the natural logarithms.

By substituting these values, we have:

ln(20) = ln(250) + (t/half-life) * ln(1/2)

With the help of a scientific calculator or software, you can calculate the natural logarithms and simplify the equation to solve for 't/half-life'.

Once you have 't/half-life', you can multiply it by the actual half-life of the substance to get the total time it will take for the initial amount to decay to 20 grams.