Question

the function f(t)2200(0.9985)^t represents the change in a quantity over t months what does the constant 0.9985 reveal about the rate of change of the quantity

the function is blank exponentially at a rate of blank percent every blank

Answer 1

The function \( f(t) = 2200(0.9985)^t \) represents exponential decay because the base of the exponent, \( 0.9985 \), is less than 1.

To analyze the rate of change:

1. **Calculating the decay rate**:
The decay can be calculated as follows:

\[
\text{Decay rate} = 1 - 0.9985 = 0.0015
\]

This is the fractional decrease in the quantity each month.

2. **Converting to a percentage**:
To convert the decay rate to a percentage, multiply by 100:

\[
\text{Decay rate (percentage)} = 0.0015 \times 100 = 0.15\%
\]

So, you can fill in the blanks in your statement as follows:

- The function is **decaying exponentially** at a rate of **0.15 percent** every **month**.