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Answer :
- The initial value of Nintendo in 2002 is $c = 9,220,000$.
- The rate of decrease is $r = 0.112$.
- The equation for the value of Nintendo $t$ years after 2002 is $y = c(1 - r)^t$.
- Substituting the values, we get $y = 9,220,000(1 - 0.112)^t$, so the answer is $\boxed{y = 9,220,000(1 - 0.112)^t}$.
### Explanation
1. Understanding the Problem
We are given that Nintendo's brand value in 2002 was $9,220,000. We are also told that the value decreased by 11.2% each year. We need to write an equation of the form $y = c(1
obreak
vert m r)^t$ to model this situation, where $y$ is the value of Nintendo $t$ years after 2002.
2. Identifying the Values
The initial value, $c$, is the value in 2002, which is $9,220,000. The rate of decrease, $r$, is 11.2%, which is 0.112 as a decimal. Since the value is decreasing, we use the minus sign in the equation.
3. Forming the Equation
Substituting these values into the equation $y = c(1 - r)^t$, we get $y = 9,220,000(1 - 0.112)^t$.
4. Final Answer
Therefore, the equation that represents the value of Nintendo $t$ years after 2002 is $y = 9,220,000(1 - 0.112)^t$. Comparing this to the given options, we see that option d matches our equation.
### Examples
Imagine you are tracking the depreciation of a car's value over time. If the car's initial value was $25,000 and it depreciates at a rate of 8% per year, you can use a similar equation to predict its value after a certain number of years. This type of calculation is also useful in finance for calculating the decreasing value of investments or assets.
- The rate of decrease is $r = 0.112$.
- The equation for the value of Nintendo $t$ years after 2002 is $y = c(1 - r)^t$.
- Substituting the values, we get $y = 9,220,000(1 - 0.112)^t$, so the answer is $\boxed{y = 9,220,000(1 - 0.112)^t}$.
### Explanation
1. Understanding the Problem
We are given that Nintendo's brand value in 2002 was $9,220,000. We are also told that the value decreased by 11.2% each year. We need to write an equation of the form $y = c(1
obreak
vert m r)^t$ to model this situation, where $y$ is the value of Nintendo $t$ years after 2002.
2. Identifying the Values
The initial value, $c$, is the value in 2002, which is $9,220,000. The rate of decrease, $r$, is 11.2%, which is 0.112 as a decimal. Since the value is decreasing, we use the minus sign in the equation.
3. Forming the Equation
Substituting these values into the equation $y = c(1 - r)^t$, we get $y = 9,220,000(1 - 0.112)^t$.
4. Final Answer
Therefore, the equation that represents the value of Nintendo $t$ years after 2002 is $y = 9,220,000(1 - 0.112)^t$. Comparing this to the given options, we see that option d matches our equation.
### Examples
Imagine you are tracking the depreciation of a car's value over time. If the car's initial value was $25,000 and it depreciates at a rate of 8% per year, you can use a similar equation to predict its value after a certain number of years. This type of calculation is also useful in finance for calculating the decreasing value of investments or assets.
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