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)

Question

05-06-2017
Mathematics

contestada

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)

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jdoe0001 jdoe0001 · Answer 1 · 2017-06-06T00:10:38+02:00

[tex]\bf A=P(1+r)^x\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{starting amount}\\ r=\textit{rate of change}\\ x=\textit{elapsed time,years}\\ \end{cases}\\\\ -------------------------------\\\\ \begin{array}{llcll} f(x)=&0.69(1&+&0.03)^x\\ &P&positive&r \end{array}\implies f(x)=0.69(1.03)^x[/tex]

the rate is 0.03 in decimal format, let us change it to percentage by simply multiplying it by 100, 0.03 * 100, is 3, or 3%

the rate is positive, so is increasing