Determine whether the following represents
continuous growth, continuous decay, or neither.

Question

Determine whether the following represents continuous growth, continuous decay, or neither. $$ y=3.5(e)^{-5 t} $$

UpStudy AI · Accepted Answer

To determine whether the function $$ y = 3.5(e)^{-5t} $$ represents continuous growth, continuous decay, or neither, we can analyze the exponent of the exponential function.

1. **Identify the form of the function**: The function is in the form $$ y = a e^{kt} $$, where:
   - $$ a = 3.5 $$ (the initial value),
   - $$ k = -5 $$ (the growth/decay rate),
   - $$ t $$ is the time variable.

2. **Analyze the value of $$ k $$**:
   - If $$ k > 0 $$, the function represents continuous growth.
   - If $$ k < 0 $$, the function represents continuous decay.
   - If $$ k = 0 $$, the function is constant.

In this case, since $$ k = -5 $$ (which is less than 0), the function represents continuous decay.

Thus, the function $$ y = 3.5(e)^{-5t} $$ represents **continuous decay**.
The function $$ y = 3.5(e)^{-5t} $$ represents **continuous decay**.

Determine whether the following represents
continuous growth, continuous decay, or neither.

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