Question
A radioactive substance decays at a rate of 6% each year. If the initial amount of the substance was 600 grams, create an exponential function to model the decay of the substance. Which of the following options correctly models the decay?
Option #1: f(x)=600(0.06)x
Option #2: f(x)=600(1.06)x
Option #3: f(x)=600(0.6)x
Option #4: f(x)=600(0.94)x
(1 point)
The option that correctly models the problem is Option #
.
Option #1: f(x)=600(0.06)x
Option #2: f(x)=600(1.06)x
Option #3: f(x)=600(0.6)x
Option #4: f(x)=600(0.94)x
(1 point)
The option that correctly models the problem is Option #
.
Answers
GPT-4o mini
To model the decay of a radioactive substance that decreases at a rate of 6% each year, we can use the formula for exponential decay:
\[ f(t) = A(1 - r)^t \]
where:
- \( A \) is the initial amount,
- \( r \) is the decay rate (as a decimal),
- \( t \) is time in years.
In this case:
- \( A = 600 \) grams,
- \( r = 0.06 \).
Thus, the function becomes:
\[ f(t) = 600(1 - 0.06)^t \]
\[ f(t) = 600(0.94)^t \]
From the provided options, the correct model for the decay is:
**Option #4:** \( f(x) = 600(0.94)^x \)
So, the answer is:
**Option #4**.
\[ f(t) = A(1 - r)^t \]
where:
- \( A \) is the initial amount,
- \( r \) is the decay rate (as a decimal),
- \( t \) is time in years.
In this case:
- \( A = 600 \) grams,
- \( r = 0.06 \).
Thus, the function becomes:
\[ f(t) = 600(1 - 0.06)^t \]
\[ f(t) = 600(0.94)^t \]
From the provided options, the correct model for the decay is:
**Option #4:** \( f(x) = 600(0.94)^x \)
So, the answer is:
**Option #4**.