If a boat depreciates in value according to the formula [tex]y = 20000(0.92)^t[/tex], find the rate of decay. Show your work and write your answer as a percentage.

To find the rate of decay for the boat's value, we need to understand the formula given: [tex]\( y = 20000 \times (92)^t \)[/tex].

Here, the formula can be interpreted as the boat depreciating by a certain percentage every year.

Let's break it down step-by-step:

1. Identify the depreciation factor:
- The formula shows [tex]\( y = 20000 \times (92/100)^t \)[/tex].
- Here, [tex]\( 92/100 \)[/tex] represents how the boat's value changes each year in terms of a factor.

2. Calculate the depreciation factor:
- The depreciation factor is [tex]\( \frac{92}{100} = 0.92 \)[/tex].
- This means that each year, the boat retains 92% of its value from the previous year.

3. Find the rate of decay:
- The rate of decay is the percentage of the value that the boat loses each year.
- Since the boat retains 92% of its value each year, the part of the value it loses is [tex]\( 1 - 0.92 = 0.08 \)[/tex].

4. Express the rate of decay as a percentage:
- Convert that decimal to a percentage by multiplying by 100: [tex]\( 0.08 \times 100 = 8\%\)[/tex].

Therefore, the rate of decay of the boat is 8%. This means the boat loses 8% of its value each year.