Answer :
To find the rate of decay for the boat’s depreciation, we can use the formula provided: [tex]\( y = 20000(0.92)^t \)[/tex].
Here's how to find the rate of decay step-by-step:
1. Identify the Decay Factor:
- In the formula [tex]\( y = a(b)^t \)[/tex], the term [tex]\( b \)[/tex] represents the decay factor. Here, the decay factor [tex]\( b \)[/tex] is 0.92.
2. Calculate the Decay Rate:
- The decay rate is found by subtracting the decay factor from 1. This represents the fraction of value the boat loses each year.
- Decay rate = [tex]\( 1 - 0.92 \)[/tex].
3. Convert the Decay Rate to a Percentage:
- To express the decay rate as a percentage, multiply it by 100.
- Decay rate percentage = [tex]\( (1 - 0.92) \times 100 \)[/tex].
4. Final Calculation:
- [tex]\( 1 - 0.92 = 0.08 \)[/tex]
- [tex]\( 0.08 \times 100 = 8 \)[/tex]
Therefore, the rate of decay is 8%. The boat's value decreases by 8% each year.
Here's how to find the rate of decay step-by-step:
1. Identify the Decay Factor:
- In the formula [tex]\( y = a(b)^t \)[/tex], the term [tex]\( b \)[/tex] represents the decay factor. Here, the decay factor [tex]\( b \)[/tex] is 0.92.
2. Calculate the Decay Rate:
- The decay rate is found by subtracting the decay factor from 1. This represents the fraction of value the boat loses each year.
- Decay rate = [tex]\( 1 - 0.92 \)[/tex].
3. Convert the Decay Rate to a Percentage:
- To express the decay rate as a percentage, multiply it by 100.
- Decay rate percentage = [tex]\( (1 - 0.92) \times 100 \)[/tex].
4. Final Calculation:
- [tex]\( 1 - 0.92 = 0.08 \)[/tex]
- [tex]\( 0.08 \times 100 = 8 \)[/tex]
Therefore, the rate of decay is 8%. The boat's value decreases by 8% each year.
