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Answer :
To solve this problem, we're looking for the value of [tex]\( b \)[/tex] in the equation [tex]\( y = 20000(b)^x \)[/tex], and we know the truck depreciates at a rate of 11% annually.
1. Understand Depreciation: Depreciation means that the truck loses value each year. Specifically, the truck loses 11% of its value annually.
2. Find the Remaining Value Percentage: If the truck loses 11% of its value, then it retains 100% - 11% = 89% of its value each year.
3. Convert Percentage to Decimal: The 89% retention of value needs to be expressed as a decimal to be used in the equation. So, 89% becomes 0.89.
4. Determine the Value of [tex]\( b \)[/tex]: In the equation [tex]\( y = 20000(b)^x \)[/tex], [tex]\( b \)[/tex] represents the factor by which the truck's value is multiplied each year. Since the truck retains 89% of its value each year, [tex]\( b \)[/tex] is 0.89.
Therefore, the value of [tex]\( b \)[/tex] in the equation is 0.89.
1. Understand Depreciation: Depreciation means that the truck loses value each year. Specifically, the truck loses 11% of its value annually.
2. Find the Remaining Value Percentage: If the truck loses 11% of its value, then it retains 100% - 11% = 89% of its value each year.
3. Convert Percentage to Decimal: The 89% retention of value needs to be expressed as a decimal to be used in the equation. So, 89% becomes 0.89.
4. Determine the Value of [tex]\( b \)[/tex]: In the equation [tex]\( y = 20000(b)^x \)[/tex], [tex]\( b \)[/tex] represents the factor by which the truck's value is multiplied each year. Since the truck retains 89% of its value each year, [tex]\( b \)[/tex] is 0.89.
Therefore, the value of [tex]\( b \)[/tex] in the equation is 0.89.
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