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100 POINTSSS! ASAP ANSWEERR PLS The price of products may increase due to inflation and decrease due to depreciation. Marco is studyi
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100 POINTSSS! ASAP ANSWEERR PLS
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
Which product recorded a greater percentage change in price over the previous year? Justify your answer.
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Mathematics
3 years
2021-08-16T22:07:04+00:00
2021-08-16T22:07:04+00:00 1 Answers
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Answers ( )
PART A
Given:
f(x) = 0.69(1.03)x
To find:
If the price of the product is increasing or decreasing and by what percentage
Steps:
we know the formula to find the price of Product A per year, so
f(1) = 0.69 * 1.03 * 1
Price = $0.7107
f(2) = 0.69 * 1.03 * 2
Price = $1.4214
Here the Price of Product after 2 years is greater than the price of Product after one year. So the price of the product A is increasing.
Now to find percentage increase,
Percentage increase =
(FV = final value, SV = starting value)
Percentage increase =![Rendered by QuickLaTeX.com \frac{1.4214 - 0.7107}{0.7107}*100](https://documen.tv/wp-content/ql-cache/quicklatex.com-766cae1bfbccc88c3aa3bdd326b87bfd_l3.png)
Percentage increase =![Rendered by QuickLaTeX.com \frac{0.7107}{0.7107}*100](https://documen.tv/wp-content/ql-cache/quicklatex.com-53ea7044fe2d9f82688fe559fd8920e0_l3.png)
Percentage increase = 100 %
Therefore, the percentage increase of Product A is 100%
PART B
Given:
Price of product B in 1st year = $10,100
Price of product B in 2nd year = $10,201
Price of product B in 3rd year = $10,303.01
Price of product B in 4th year = $10,406.04
To find:
Which product recorded a greater percentage change over the previous year
Steps:
We need to find the percentage change of Product B and Product A of each year. We know that the percentage change of product A is 100 % for each year, so we only need to calculate for product B
PC of product B from 1st to 2nd year =![Rendered by QuickLaTeX.com \frac{10,201-10,100}{10,100}*100](https://documen.tv/wp-content/ql-cache/quicklatex.com-e87a365250714133e718601246c1895a_l3.png)
=![Rendered by QuickLaTeX.com \frac{101}{10,100}*100](https://documen.tv/wp-content/ql-cache/quicklatex.com-c07655018898018ba3f188ff6d2a914f_l3.png)
= 0.01 * 100
= 1 %
PC of product B from 2nd to 3rd year =![Rendered by QuickLaTeX.com \frac{10,303.01-10,201}{10,201} *100](https://documen.tv/wp-content/ql-cache/quicklatex.com-cd4f5f80379148a7a8e72881c3d3d42d_l3.png)
= 1%
PC of product B from 3rd to 4th year![Rendered by QuickLaTeX.com =\frac{10,406.04-10,303.01}{10,303.01}*100](https://documen.tv/wp-content/ql-cache/quicklatex.com-d1e3b223dc28cc836b677fb989a930b1_l3.png)
≈ 1%
So, percentage change of product B is 1% per year
Therefore, Product A has greater percentage change
Happy to help 🙂
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