Question

Helppp meeee AI keeps getting it wrong

Answer 1

The exponential decay function for the mass of the substance (y) in terms of the number of years (t) since 2000 is
`\[ y = 400 \cdot (1 - 0.039)^t \]`

The exponential decay model can be expressed using the formula:

`\[ y = y_0 \cdot (1 - r)^t \]`

where:

- y is the final amount,

-
`\( y_0 \)` is the initial amount,

- r is the decay rate per time period,

- t is the number of time periods.

In this scenario:

-
`\( y_0 = 400 \)` milligrams (initial mass in 2000),

- r = 0.039 (3.9% decay per year),

- t is the number of years since 2000.

Therefore, the exponential decay function for the mass of the substance (y) in terms of the number of years (t) since 2000 is:

`\[ y = 400 \cdot (1 - 0.039)^t \]`