Question

The function f, of, t, equals, 570, left parenthesis, 0, point, 8, right parenthesis, to the power tf(t)=570(0.8)
t
represents the change in a quantity over t years. What does the constant 0.8 reveal about the rate of change of the quantity?
Answer
Attempt 1 out of 2

The function is
exponentially at a rate of
% every
.

Answer 1

The function \( f(t) = 570(0.8)^t \) represents exponential decay, where \( 570 \) is the initial quantity and \( 0.8 \) is the decay factor.

To understand what the constant \( 0.8 \) reveals about the rate of change:

1. **Decay Factor**: The constant \( 0.8 \) indicates that each year, the quantity retains \( 80\% \) of its value from the previous year. This means that the quantity decreases by \( 20\% \) every year.

2. **Rate of Change**: Since \( 0.8 \) reflects the remaining proportion of the quantity, the rate of change can be computed as:
\[
\text{Rate of decay} = 1 - 0.8 = 0.2 \, \text{or} \, 20\%
\]

Therefore, the function is decaying exponentially at a rate of **20%** every **year**.

In summary, you can complete your answer as follows:

The function is decaying exponentially at a rate of **20%** every **year**.