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

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.