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) = 12500(0.82)x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? [
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) 5600 3136 1756.16 983.45
Which product recorded a greater percentage change i

Answer 1

Well, it's increasing because the slope of the line is positive. In order to find out how much it is increasing, you have to find 2 points on that line. You can do that by doing an x/y chart; use a value for x and then determine what the y value is. When you have two points, assuming the graph is linear, you can find the slope. The change in y is your rate of change in the increase of the price in dollars. See that? So let's first find out (or make sure) that this is linear. If it's not, then the rate of change isn't constant.

Answer 2

Wait...is the function this:\[f(x)=12500(.82)x\]or is it this:\[f(x)=12500(.82)^{x}\]

Answer 3

Because the first one is linear but the second one is exponential.

Answer 4

exponential

Answer 5

@IMStuck

Answer 6

@IMStuck are you still there??

Answer 7

First you have to mult this:
A --- 12500 * 0.82 times year 2 would be 12500 * 0.82^2 would be 12500 * 1.62=20,250 so we know know that it is increasing, right?
so the would look like f(x) = 10250 * 0.63x <---- is a linear .
We know that the coefficient of x is positive, so that way we know that the function is increasing :)

Answer 8

i understand, but part b is really confusing

Answer 9

wait (0.82) is less than 1, so isn't it decreasing?

Answer 10

by 24% each year

Answer 11

oh i might have made a mistake :/

Answer 12

lol its ok it happens to the best of us! can you explain part b

Answer 13

@superhelp101