Answer:
328.05 dollars
7 years
Explanation:
1.
y=500(.9)^4 =328.05
What is being asked in the problem and what does that mean?
We are asked to the price of the video game after 4 years.
What do I know and what does it mean? What plan am I going to try?
We know the initial price is $500, the value depreciates 10% each year because we have .9 or 90% of the price going into the next year.
- value of the video game after first year 90% of 500 so is 450
- value of the video game after second year 90% of 450 so is 405
-value of the video game after third year 90% of 405 so is 364.5
-value of the video game after fourth year 90% of 364.5 so is 328.05
The plan is to substitute x with 4 and calculate y, y=500(.9)^4
What is your answer and what does it mean?
The answer is $328.05, and it means that the video game that was initially worth $500 it lost its' value by 10 % each of the four years.
2.
y= 500(.9)^x
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x =8, y= 500(0.9)^8 = 215.234 ≈215.23, this is less than $250
x = 7, y= 500(0.9)^7 = 239.148 ≈239.15, this is less than $250
x =6, y= 500(0.9)^6 = 265.721 ≈ 265.72, this is more than $250
What is being asked in the problem and what does that mean?
We are asked to find the value of x that represents the years such that the value of the console is still under $250.
What do I know and what does it mean? What plan am I going to try?
We know the value of y has to be less that $250, we know the inequality
[500(.9)^x ] < 250, the plan is to try different values for x until we have the maximum value of x that gives us less than 250.