Question

A substance decays at 6% each year if the initial amount of the substance was 600 grams create an exponential function to model the decay
f(x)=600(0.06)^
600(.40)^x
600(0.6)^x
600(0.94)^x

Answer 1

To create an exponential function to model the decay of a substance that decays at a rate of 6% each year, we start with the initial amount and determine the decay factor.

1. **Initial amount:** 600 grams
2. **Decay rate:** 6% means that each year, 94% of the substance remains (100% - 6% = 94%).

The decay factor can be expressed as a decimal:

\[
\text{Decay factor} = 1 - 0.06 = 0.94
\]

Now, we can use the general formula for exponential decay:

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

where:
- \( A \) is the initial amount,
- \( r \) is the decay factor,
- \( x \) is the number of years.

Substituting in the values we have:

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

Therefore, the correct exponential function that models the decay of the substance is:

\[
\boxed{600(0.94)^x}
\]