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notsponge [240]
2 years ago
7

The cost of a High Definition television now averages $700, but the cost is decreasing about 15% per year. In how many years wil

l the cost be under $200?
Mathematics
1 answer:
Roman55 [17]2 years ago
3 0

Answer: 7.7 years

Step-by-step explanation:

Given

The cost of HD TV is $700 and it is decreasing at the rate of 15% per year

After one year it becomes

\Rightarrow 700-700\times 15\%\\\Rightarrow 700(1-0.15)

after 2 year it becomes

\Rightarrow 700(1-0.15)-700(1-0.15)\times 15\%\\\Rightarrow 700(1-0.15)(1-0.15)\\\Rightarrow 700(1-0.15)^2

Suppose, after x years it becomes $200

\Rightarrow 200=700(1-0.15)^x\\\\\Rightarrow \dfrac{2}{7}=0.85^x\\\\\text{Taking log both sides}\\\\\Rightarrow x=\dfrac{\ln (\frac{2}{7})}{\ln (0.85)}\\\\\Rightarrow x=7.7\ \text{years}

Thus, it takes 7.7 years for the cost to come under $200.

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At a sale this week, a desk is being sold for 128.80. This is a 72% discount from the original price. What is the original price
wel

Answer:

$460

Step-by-step explanation:

If the 128.80 is the price of the desk after a 72% discount, it means that 128.80 is 100-72=28% of the original price.

From here, we can divide 128.80 by 28 to find what 1% of the price is then multiply the value by 100 to find 100%, or the original price.

128.80/28 = 4.6

4.6 x 100 = 460

Original price = $460

Hope this helped!

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2 years ago
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Answer:

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3 years ago
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