To determine the base that models a 15% decay in the exponential function, let's go through the decay process step-by-step.
1. Understand the concept of decay rate: A 15% decay means that each period, the quantity decreases by 15%.
2. Express decay rate in decimal form: 15% corresponds to [tex]\( 0.15 \)[/tex] in decimal form.
3. Determine the remaining quantity after one period: If a quantity decreases by 15%, the remaining fraction of the quantity is [tex]\( 1 - 0.15 \)[/tex].
4. Calculate this remaining fraction:
[tex]\[
1 - 0.15 = 0.85
\][/tex]
Therefore, the base that should be written in the blank to model a 15% decay is [tex]\( 0.85 \)[/tex].
So, the exponential decay function can be written as:
[tex]\[ y = (0.85)^{\frac{t}{12}} \][/tex]
