Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of change.



A
Exponential decay; 8.5%

B
Exponential decay; 8%

C
Exponential growth; 8%

D
Exponential growth; 8.5%

1 answer

To determine whether a function represents exponential growth or decay and to find the percentage rate of change, we need to analyze the function. Typical forms of exponential functions are:

  1. \( f(t) = a \cdot e^{kt} \) or \( f(t) = a(1 + r)^t \) for growth (where \( r \) is positive).
  2. \( f(t) = a \cdot e^{-kt} \) or \( f(t) = a(1 - r)^t \) for decay (where \( r \) is positive).

The sign of the exponent (either \( k \) or \( -k \)) indicates growth or decay:

  • If \( k > 0 \), it's exponential growth.
  • If \( k < 0 \) (or if \( r > 0 \) and we're subtracting), it's exponential decay.

To find the rate of change:

  • The percentage rate of change \( r \) in an exponential growth function is simply taken from the coefficient in front of the exponential term or the base, as \( (1 + r) \) or \( (1 - r) \).

Without the specific function provided, I cannot definitively categorize it as exponential growth or decay or determine the percentage rate of change.

If you provide the exact function or equation, I can analyze it accordingly and choose the correct option among A, B, C, or D.