Question

melanie 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 melanie started studying the sample, and the total mass remaining in the sample, m(t), in micrograms, is modeled by the following function: m(t) = 169·(0.96)^t complete the following sentence about the daily percent change in the mass of the sample. every day, 96 % of mass is subtracted from the total mass of the sample. related content interpreting change in exponential models

Explanation:

Step1: Identify decay factor form

Exponential decay model: $M(t) = M_0(1-r)^t$

Step2: Match to given function

Given $M(t)=169\cdot(0.96)^t$, so $1-r=0.96$

Step3: Solve for decay rate $r$

$r=1-0.96=0.04=4\%$

Step4: Interpret the rate

A 4% decay means 4% is subtracted daily.

Answer:

Every day, $\boldsymbol{4}$% of mass is $\boldsymbol{subtracted from}$ the total mass of the sample.