Question

Einsteinium-253 is an element that loses about 2/3 of its mass every month. A sample of einsteinium-253 has 450 grams. Write a function that gives the samples mass in grams, s(t), t months from today.

Answer 1

The exponential function that gives the sample mass in grams is:

$s(t) = 450\left(\frac{1}{3}\right)^t$

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:

• Einsteinium-253 is an element that loses about 2/3 of its mass every month, hence $r = \frac{2}{3}$.

• A sample of einsteinium-253 has 450 grams, hence A(0) = 450.

Then, the mass is given by:

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

$s(t) = 450\left(1 - \frac{2}{3}\right)^t$

$s(t) = 450\left(\frac{1}{3}\right)^t$

More can be learned about exponential functions at https://brainly.com/question/25537936