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. (1 point)
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Equation that correctly models the decay: Response area

Answer 1

The exponential decay function can be modeled with the formula:

\[ A(t) = A_0 \cdot (1 - r)^t \]

Where:

• \( A(t) \) is the amount of substance remaining after time \( t \),
• \( A_0 \) is the initial amount of the substance,
• \( r \) is the decay rate (as a decimal),
• \( t \) is the time in years.

Given:

• The initial amount \( A_0 = 600 \) grams,
• The decay rate \( r = 0.06 \) (which represents 6%).

Substituting the known values into the formula gives:

\[ A(t) = 600 \cdot (1 - 0.06)^t \]

This can be simplified to:

\[ A(t) = 600 \cdot (0.94)^t \]

So the equation that correctly models the decay is:

Response area:

\[ A(t) = 600 \cdot (0.94)^t \]