Final answer:
To find the remaining milligrams of a decaying substance by 2028, calculate the decay constant using the exponential decay formula and the data from 2009 to 2017, and then apply this constant to predict the quantity in 2028.
Step-by-step explanation:
The question involves calculating the remaining quantity of a chemical substance after a certain period, given its exponential decay rate. We are given that 31 mg of a substance decayed to 24 mg from 2009 to 2017. To predict the remaining mass in 2028, we initially need to determine the decay rate using the provided information. As we know that decay follows an exponential function of the form N(t) = N_0 e^{-kt}, where N_0 is the initial quantity of the substance, N(t) is the quantity after time t, and k is the decay constant. Once k is found, we can calculate the predicted mass remaining in 2028.
Step 1: Find the decay constant k using the initial and final quantity (31 mg to 24 mg) and the time period (8 years).
Step 2: Use the decay formula with the calculated value of k to find the quantity that remains in 2028, which is 19 years after 2009.