Question

Clemence began studying a sample of the chemical element einsteinium- 253 253253, which naturally loses its mass over time. The relationship between the elapsed time, t tt, in days, since Clemence started studying the sample, and the total mass remaining in the sample, M ( t ) M(t)M, left parenthesis, t, right parenthesis, 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.

Answer 1

Using exponential function concepts, it is found that the daily rate of change in the mass of the sample is of -4%, that is, the amount decays by 4%.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem, the function is:

$M(t) = 200(0.96)^t$

Hence:

$1 - r = 0.96$

$r = 0.04$

1 - r < 1, hence the rate is negative, and the daily rate of change in the mass of the sample is of -4%.

You can learn more about exponential function concepts at brainly.com/question/25537936