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

The function given is:

$$ y = 3.5e^{-5t} $$

This is an exponential function of the form:

$$ y = Ce^{kt} $$

where:
- $$ C = 3.5 $$ is the initial value,
- $$ k = -5 $$ is the growth (if positive) or decay (if negative) rate.

### Analyzing the Exponent $$ k $$:

- **If $$ k > 0 $$**: The function represents **continuous growth** because the exponent is positive, causing the function to increase exponentially as $$ t $$ increases.
  
- **If $$ k < 0 $$**: The function represents **continuous decay** because the exponent is negative, causing the function to decrease exponentially as $$ t $$ increases.

- **If $$ k = 0 $$**: The function is constant, neither growing nor decaying.

In the given function:

$$ k = -5 $$

Since $$ k $$ is negative, the function represents **continuous decay**.

### Conclusion:

The function $$ y = 3.5e^{-5t} $$ describes continuous decay.

**Answer:** It describes a situation of continuous exponential decay.
The function $$ y = 3.5e^{-5t} $$ represents **continuous decay**.

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

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Solución

Analyzing the Exponent :

Conclusion:

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