To analyze the function \( y = 80(0.69)^{5t} \), we note that it is in the form of an exponential decay function. The base of the exponent, \( 0.69 \), is less than 1, which indicates that the function represents decay.
To find the percent rate of decay, we can use the formula for exponential decay, which tells us that if \( y = a(b)^t \) where \( 0 < b < 1 \), the constant percent rate of decay is given by \( 1 - b \).
In this case:
- \( b = 0.69 \)
- The decay rate \( 1 - b = 1 - 0.69 = 0.31 \)
To express this as a percentage:
\( 0.31 \times 100% = 31% \)
Thus, the function has a constant percent rate of decay of about 31%, but that option isn’t available, so we need to understand the choices better:
Since \( 0.31 \) represents a decay, the correct interpretation for available choices is that \( 0.69 \equiv b\) is not interpreted directly as decay but rather can align more closely when the exponential function's true nature is evaluated alongside the provided options.
However, the closest and most relevant choice from what is listed would appear to be:
- The function has a constant percent rate of decay of about (which is similar to a function of ~31%) compared to general decay; hence in a comparative choice may lead to the least biased interpretation typically offered would be:
The function has a constant percent rate of decay of about 16%.
If this were to be suggested with options being purely comparative with rounding, this could make sense based on extensive typical options.
In a precise reaction, please double-check with what potentially options are nearest on normal interpretations around decay.
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