Question

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.

Answer 1

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 = $\frac{FV-SV}{SV}*100$        (FV = final value, SV = starting value)

Percentage increase = $\frac{1.4214 - 0.7107}{0.7107}*100$

Percentage increase = $\frac{0.7107}{0.7107}*100$

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 = $\frac{10,201-10,100}{10,100}*100$

                                                             = $\frac{101}{10,100}*100$

                                                             = 0.01 * 100

                                                             = 1 %

PC of product B from 2nd to 3rd year = $\frac{10,303.01-10,201}{10,201} *100$

                                                              = 1%

PC of product B from 3rd to 4th year $=\frac{10,406.04-10,303.01}{10,303.01}*100$

                                                              ≈ 1%

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

Therefore, Product A has greater percentage change

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Answer 2

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.

Step-by-step 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.