There was a sample of 900 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by
each year.
Let be the number of years since the start of the study. Let be the mass of the sample in milligrams.
Write an exponential function showing the relationship between and .
.

Ask by Harmon Byrd. in the United States

Mar 15,2025

Question

There was a sample of 900 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by
each year.
Let be the number of years since the start of the study. Let be the mass of the sample in milligrams.
Write an exponential function showing the relationship between and .
.

Ask by Harmon Byrd. in the United States

Mar 15,2025

UpStudy AI · Accepted Answer

To model the decay of a radioactive substance, we can use the exponential decay formula:

$$
y = y_0 \cdot (1 - r)^t
$$

where:
- $$ y $$ is the remaining mass of the substance after $$ t $$ years,
- $$ y_0 $$ is the initial mass of the substance,
- $$ r $$ is the decay rate (as a decimal),
- $$ t $$ is the time in years.

Given the problem:
- The initial mass $$ y_0 = 900 $$ milligrams,
- The decay rate $$ r = 7.4\% = 0.074 $$.

Now, we can substitute these values into the formula:

$$
y = 900 \cdot (1 - 0.074)^t
$$

This simplifies to:

$$
y = 900 \cdot (0.926)^t
$$

Thus, the exponential function showing the relationship between $$ y $$ and $$ t $$ is:

$$
y = 900 \cdot (0.926)^t
$$
The relationship between $$ y $$ and $$ t $$ is $$ y = 900 \times (0.926)^t $$.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Pre Calculus Questions