Question

clemence began studying a sample of the chemical element einsteinium-253, which naturally loses its mass over time. the relationship between the elapsed time, t, in days, since clemence started studying the sample, and the total mass remaining in the sample, m(t), in milligrams, is modeled by the following function: m(t) = 200·(0.96)^t complete the following sentence about the daily rate of change in the mass of the sample. every day, the mass of the sample grows/shrinks by a factor of.

Explanation:

Step1: Identify exponential model form

The given function is $M(t) = 200 \cdot (0.96)^t$, which follows the exponential decay/growth form $M(t) = M_0 \cdot r^t$, where $r$ is the daily factor.

Step2: Analyze the base value

Since $0 < 0.96 < 1$, this indicates a decrease (shrinking) in mass over time. The base $0.96$ is the factor by which the mass changes daily.

Answer:

Every day, the mass of the sample shrinks by a factor of $0.96$.