3. Take a look at the student's solution below. If they are incorrect, explain what error(s) the student made and how to correctly solve the problem (step-by-step):

3. The radioactive isotope radium-226 has a half-life of 1600 years. After 8,000 years there is 30 milligrams of radum-226, how many milligrams will there be after 3200 years? Student's Solution: Step 1: Let t be the number of years. We are given that the amount of radium-226 at time t = 8000 is 30 mg, and that the half-life of radium-226 is 1600 years. Step 2: Because the half-life is 1600 years, we know that at time t = 8000 - 1600 = 6400 years, the amount is 30 x 2 = 60 mg. 60 - 30 -3 Step 3: Therefore, the exponential rate of change is calculated as 6400 - 8000 160 mg/year. -3 Step 4: At 1 = 3200, the amount is 30 mg + (3200 - 8000) years x 160 mg/year = 120 mg