Question

The price of products may increase due to inflation and decrease due to depreciation. Derek 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. (5 points)

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. (5 points)

Please Help :(

Answer 1

Product A is increasing because the base 1.03 in the exponential is greater than 1.

The percent increase is $(1.03-1)*100\%=0.03*100\%=3\%$ per year.

For product B, the rate of increase is $\frac{10,201}{10,100}=1.01$

The percent increase is $(1.01-1)*100\%=0.01*100\%=1\%$ per year.

Product A has a higher percent increase.

Answer 2

Answer:

Product A's price has the greatest percentage in change. 3% increase is more than 1% increase.

Step-by-step explanation:

Part A:

f(x) = 0.69(1.03)x

1 year= 0.69(1.03)1= 0.7107

2 years= 0.69(1.03)2 = 0.732021

3 years= 0.69(1.03)3= 0.75398163  

4 years= 0.69(1.03)4= 0.776601078

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

Part B:

Percent change:

Year 2: 10,201 / 10,100 = 1.01

Year 3: 10,303.01 / 10,201 = 1.01

Year 4: 10,406.04 / 10,303.01 = 1.01

The price for product B has increased by 1% every year.

Product A's price has the greatest percentage in change. 3% increase is more than 1% increase.