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?(1 point)
Responses
f(x)=600(0.06)x
f of x is equal to 600 times 0 point 0 6 to the x th power
f(x)=600(1.06)x
f of x is equal to 600 times 1 point 0 6 to the x th power
f(x)=600(0.6)x
f of x is equal to 600 times 0 point 6 to the x th power
f(x)=600(0.94)x
Responses
f(x)=600(0.06)x
f of x is equal to 600 times 0 point 0 6 to the x th power
f(x)=600(1.06)x
f of x is equal to 600 times 1 point 0 6 to the x th power
f(x)=600(0.6)x
f of x is equal to 600 times 0 point 6 to the x th power
f(x)=600(0.94)x
Answers
GPT-4o mini
To model the decay of the radioactive substance, we need to use an exponential decay function. The general formula for exponential decay is:
\[
f(x) = a(1 - r)^x
\]
where:
- \( a \) is the initial amount,
- \( r \) is the decay rate (as a decimal), and
- \( x \) is the time in years.
In this case:
- The initial amount \( a = 600 \) grams.
- The decay rate \( r = 6\% = 0.06 \).
Thus, the function becomes:
\[
f(x) = 600(1 - 0.06)^x = 600(0.94)^x
\]
Therefore, the correct option to model the decay of the substance is:
**f(x) = 600(0.94)^x**
\[
f(x) = a(1 - r)^x
\]
where:
- \( a \) is the initial amount,
- \( r \) is the decay rate (as a decimal), and
- \( x \) is the time in years.
In this case:
- The initial amount \( a = 600 \) grams.
- The decay rate \( r = 6\% = 0.06 \).
Thus, the function becomes:
\[
f(x) = 600(1 - 0.06)^x = 600(0.94)^x
\]
Therefore, the correct option to model the decay of the substance is:
**f(x) = 600(0.94)^x**