A sample of 100 mg of cobalt is studied over time. After 1 year, the sample was measured at 97.5 mg. If the size of the sample continues to change at the same rate, which equation models the change?

The equation modeling the change in mass of the cobalt sample over time, with a constant rate of decrease, is M = 100 - 2.5t, where M is the final mass and t is time in years.

Explanation:

The question involves finding an equation that models the change in mass of a cobalt sample over time, assuming a constant rate of decrease. In one year, the mass of cobalt decreased from 100 mg to 97.5 mg, which is a change of 2.5 mg per year.

To find a general equation for the mass at any given time, we use the formula M = M0 - rt, where M is the final mass, M0 is the initial mass, r is the rate of change, and t is time in years. Since we know M0 = 100 mg and r = 2.5 mg/year, the equation becomes M = 100 - 2.5t. This linear equation models the change in mass of the cobalt sample over time, assuming the same rate of decrease continues.