Einsteinium-253 is an element that loses about (2)/(3) of its mass every month. A sample of Einsteinium253 has 450 grams. Write a function that gives the sample's mass in grams, S(t),t months from today. S(t)=

Identify initial mass and decay rate: Step 1: Identify the initial mass and the decay rate. The initial mass of the sample is given as 450 grams. The decay rate is 2/3 of its mass every month, which means that the sample retains 1 - 2/3 = 1/3 of its mass each month. Write exponential decay function: Step 2: Write the exponential decay function. The general form of an exponential decay function is S(t) = S_0 * (decay factor)^(t), where S_0 is the initial mass and the decay factor is the fraction of mass that remains after each time period. In this case, the decay factor is 1/3. Substitute known values: Step 3: Substitute the known values into the decay function. The initial mass S_0 is 450 grams, and the decay factor is 1/3. Therefore, the function that models the mass of the sample after t months is S(t) = 450 * (1/3)^(t). Simplify function: Step 4: Simplify the function if necessary. In this case, the function is already in its simplest form, so no further simplification is needed.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Einsteinium-253 is an element that loses about
(2)/(3) of its mass every month. A sample of Einsteinium253 has 450 grams.
Write a function that gives the sample's mass in grams,
S(t),t months from today.

S(t)=

Einsteinium $-253$ is an element that loses about $\frac{2}{3}$ of its mass every month. A sample of Einsteinium $253$ has $450$ grams. $\newline$ Write a function that gives the sample's mass in grams, $S(t), t$ months from today. $\newline$ $S(t)=\square$

View step-by-step help

Home

Math Problems

Algebra 2

Interpret the exponential function word problem

Full solution

Q. Einsteinium

-253

is an element that loses about

\frac{2}{3}

of its mass every month. A sample of Einsteinium

253

has

450

grams.

\newline

Write a function that gives the sample's mass in grams,

S(t), t

months from today.

\newline

S(t)=\square

Identify initial mass and decay rate: Step $1$ : Identify the initial mass and the decay rate. The initial mass of the sample is given as $450$ grams. The decay rate is $\frac{2}{3}$ of its mass every month, which means that the sample retains $1 - \frac{2}{3} = \frac{1}{3}$ of its mass each month.
Write exponential decay function: Step $2$ : Write the exponential decay function. The general form of an exponential decay function is $S(t) = S_0 \times (\text{decay factor})^{t}$ , where $S_0$ is the initial mass and the decay factor is the fraction of mass that remains after each time period. In this case, the decay factor is $\frac{1}{3}$ .
Substitute known values: Step $3$ : Substitute the known values into the decay function. The initial mass $S_0$ is $450$ grams, and the decay factor is $\frac{1}{3}$ . Therefore, the function that models the mass of the sample after $t$ months is $S(t) = 450 \times \left(\frac{1}{3}\right)^t$ .
Simplify function: Step $4$ : Simplify the function if necessary. In this case, the function is already in its simplest form, so no further simplification is needed.