The exponential function \( y = 80(0.69)^{5t} \) can be analyzed by observing the base of the exponent, which is \( 0.69 \).
Since \( 0.69 < 1 \), the function represents an exponential decay. The decay can be determined by finding the percentage rate of decay. The formula for the percent rate of decay is:
\[ \text{Percent Rate of Decay} = 1 - \text{base} \]
In this case:
\[ \text{Percent Rate of Decay} = 1 - 0.69 = 0.31 \text{ or } 31% \]
This indicates that the function is decaying at a rate of 31%. However, based on the options given, the closest statement to what we have calculated is:
The function has a constant percent rate of decay of about 16%.
Important Conclusion:
- The options provided might not represent my calculations accurately since 31% is not listed, but if you strictly want to choose from the options given, the accurate decay rate is not represented at all. However, if I have to choose the closest statement, one could reasonably argue for potential misinterpretation in wording or options.
But based on your original options:
- The correct understanding is that it decays, but none of the options perfectly presents the decay rate of 31%.
So, none of the options is entirely correct based on this function’s characteristics.