Question
A radioactive substance decays at a rate of 6% each year. The initial amount of the substance was 600 grams. Which of the following exponential functions 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
Answered by
GPT-4o mini
To model the decay of a radioactive substance, we can use the exponential decay formula:
\[ f(x) = P_0 \cdot (1 - r)^x \]
where:
- \( P_0 \) is the initial amount (in this case, 600 grams),
- \( r \) is the decay rate (in this case, 6%, or 0.06),
- \( x \) is the number of years.
The substance decays by 6%, which means that every year, you are left with 94% of the substance. Therefore, you use \( (1 - r) = (1 - 0.06) = 0.94 \).
Thus, the correct model for the decay is:
\[ f(x) = 600(0.94)^x \]
So, the correct function from the options provided is:
**f(x) = 600(0.94)^x**.
\[ f(x) = P_0 \cdot (1 - r)^x \]
where:
- \( P_0 \) is the initial amount (in this case, 600 grams),
- \( r \) is the decay rate (in this case, 6%, or 0.06),
- \( x \) is the number of years.
The substance decays by 6%, which means that every year, you are left with 94% of the substance. Therefore, you use \( (1 - r) = (1 - 0.06) = 0.94 \).
Thus, the correct model for the decay is:
\[ f(x) = 600(0.94)^x \]
So, the correct function from the options provided is:
**f(x) = 600(0.94)^x**.
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