clemence began studying a sample of the chemical element einsteinium-253, which naturally loses its mass…

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.

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.

Answer

Explanation:

Step1: Identify the function type

The function ( M(t) = 200 \cdot (0.96)^t ) is an exponential function of the form ( M(t)=a\cdot b^t ), where ( a = 200 ) (initial mass) and ( b = 0.96 ) (the base of the exponential).

Step2: Analyze the base of the exponential

For an exponential function ( y = a\cdot b^t ), if ( 0 < b < 1 ), the function represents decay (shrinking), and the factor by which it changes per unit time (here, per day) is ( b ). Since ( 0.96< 1 ), the mass shrinks, and the factor is ( 0.96 ).

Answer:

shrinks, ( 0.96 )