Question

question
the function $f(t) = 570(0.8)^t$ 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 $quad$ exponentially at a rate of $quad$% every $quad$.

Explanation:

Step1: Identify Function Type

The function \( f(t) = 570(0.8)^t \) is an exponential function. Exponential decay has a base \( 0 < b < 1 \), here \( b = 0.8 \).

Step2: Calculate Decay Rate

For exponential decay \( f(t)=a(1 - r)^t \), compare with \( 570(0.8)^t=570(1 - r)^t \). So \( 1 - r = 0.8 \), solve for \( r \): \( r = 1 - 0.8 = 0.2 \), which is \( 20\% \) decay per year.

Answer:

The function is decaying exponentially at a rate of \( 20\% \) every year.