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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.

User Kurrodu
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2 Answers

16 votes
16 votes

Answer:

A) The price of product A is increasing by 3% per year.

(B) The product A recorded a greater percentage change in price over the previous year.

Explanation:

(A)

The function representing the price, in dollars, of product A after x years is:

FA(x)=0.69*(1.03)x

The function FA(x)can be written as:

FA(x)=0.69*1+(0.03)x

The function FA(x) is similar to the exponential growth function, y=a(1+r)x .

Here r is the growth rate.

Thus, it can be said that the price of product A is increasing by 3% per year.

(B)

Consider the data of product B for the year 3 and 4.

The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.

Compute the percent price change from year 3 to 4 as follows:

10406.04-10303.01/10303.01*100

which is 0.999%

~1%

The price of product B is increasing by 1% per year.

Thus, the product A recorded a greater percentage change in price over the previous year.

User Patrick McFadin
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3.3k points
19 votes
19 votes

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-SV)/(SV)*100 (FV = final value, SV = starting value)

Percentage increase =
(1.4214 - 0.7107)/(0.7107)*100

Percentage increase =
(0.7107)/(0.7107)*100

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 =
(10,201-10,100)/(10,100)*100

=
(101)/(10,100)*100

= 0.01 * 100

= 1 %

PC of product B from 2nd to 3rd year =
(10,303.01-10,201)/(10,201) *100

= 1%

PC of product B from 3rd to 4th year
=(10,406.04-10,303.01)/(10,303.01)*100

≈ 1%

So, percentage change of product B is 1% per year

Therefore, Product A has greater percentage change

Happy to help :)

If u need more help, feel free to ask

User Benjamin Kovach
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