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)

Question

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

Answer 1

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

\[ f(x) = A \cdot (1 - r)^x \]

where:

• \( A \) is the initial amount,
• \( r \) is the decay rate (as a decimal),
• \( x \) is the number of years.

Given that the initial amount is 600 grams and the decay rate is 6% (or 0.06 as a decimal), we can substitute these values into the formula:

1. Initial amount \( A = 600 \)
2. Decay rate \( r = 0.06 \)
3. Therefore, \( (1 - r) = (1 - 0.06) = 0.94 \)

Now, we can express the exponential decay function as:

\[ f(x) = 600 \cdot (0.94)^x \]

Thus, the correct option that models the decay is:

f(x) = 600(0.94)^x