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Question

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

Answer 1

To model the decay of a radioactive substance at a rate of 6% per year, we need to express the decay as an exponential function.

The general form for an exponential decay function is:

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

where:

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

In this case:

• The initial amount \( A = 600 \) grams,
• The decay rate \( r = 0.06 \) (which represents 6%).

Substituting these values into the formula, we have:

\[ f(x) = 600 \cdot (1 - 0.06)^x \] \[ f(x) = 600 \cdot (0.94)^x \]

Therefore, the correct function to model the decay of the substance is:

f(x) = 600(0.94)^x

So the correct answer is:

f(x) = 600(0.94)^x.