Answer :
To find the rate of decay as a percentage for a boat that depreciates in value according to the formula [tex]\( y = 20000(0.92)^z \)[/tex], follow these steps:
1. Understand the Formula:
The formula [tex]\( y = 20000(0.92)^z \)[/tex] represents the depreciation of the boat's value. Here:
- [tex]\( 20000 \)[/tex] is the initial value of the boat.
- [tex]\( 0.92 \)[/tex] is the decay factor.
2. Identify the Decay Factor:
The decay factor tells us by what fraction the value of the boat decreases each time period. In this formula, the decay factor is [tex]\( 0.92 \)[/tex].
3. Determine the Rate of Decay:
To find the rate of decay, subtract the decay factor from 1:
[tex]\[
\text{Rate of Decay} = 1 - 0.92
\][/tex]
[tex]\[
\text{Rate of Decay} = 0.08
\][/tex]
4. Convert the Rate to a Percentage:
Multiply the decimal rate of decay by 100 to convert it to a percentage:
[tex]\[
\text{Rate of Decay Percentage} = 0.08 \times 100 = 8\%
\][/tex]
Thus, the rate of decay of the boat's value is 8% per time period.
1. Understand the Formula:
The formula [tex]\( y = 20000(0.92)^z \)[/tex] represents the depreciation of the boat's value. Here:
- [tex]\( 20000 \)[/tex] is the initial value of the boat.
- [tex]\( 0.92 \)[/tex] is the decay factor.
2. Identify the Decay Factor:
The decay factor tells us by what fraction the value of the boat decreases each time period. In this formula, the decay factor is [tex]\( 0.92 \)[/tex].
3. Determine the Rate of Decay:
To find the rate of decay, subtract the decay factor from 1:
[tex]\[
\text{Rate of Decay} = 1 - 0.92
\][/tex]
[tex]\[
\text{Rate of Decay} = 0.08
\][/tex]
4. Convert the Rate to a Percentage:
Multiply the decimal rate of decay by 100 to convert it to a percentage:
[tex]\[
\text{Rate of Decay Percentage} = 0.08 \times 100 = 8\%
\][/tex]
Thus, the rate of decay of the boat's value is 8% per time period.
