Question

(FAN AND MEDAL)

Answer 1

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) = 72(1.25)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) 65 84.5 109.85 142.81


Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)

Answer 2

Part I:
You know that this function is DECREASING because 0.63, the number inside of the parenthesis, is LESS THAN THE NUMBER 1. I [think I] know the way to determine by what percentage it is decreasing. [I think] My teacher taught me that I have to subtract the number, in this case 0.63, from 1. So, 1 - 0.63 = 0.37. So it is decreasing by 0.37

Answer 3

they are all changing by the same percentage: 43% less. And you can prove it by dividing year 2 to year 1 and dividing year 3 to year 2. Sorry for the inaccurate answer

Answer 4

@chrisga

Answer 5

@campbell_st please help me! here nobody wanna help me! please help me

Answer 6

the function

f(x) is like the compound interest formula it could be written as

\[f(x) = 72 \times (1 + \frac{25}{100})^x\]

the compound interest formula is

\[A = P \times (1 + \frac{r}{100})^n\]

where r is the growth rate as a percentage

so when you compare it to your eqquation what do you think the growth rate r is..?

Answer 7

i need to solve that ?

Answer 8

90?

Answer 9

so for part A

you can write (1.25) as (1 + 0.25)

the + inside the brackets indicates its increasing and the amount of the increase is 0.25 written as a percentage

Answer 10

so the answer for part A: ITS the + inside the brackets indicates its increasing and the amount of the increase is 0.25 written as a percentage

Answer 11

?

Answer 12

and for part B?

Answer 13

part B find use the 1st 2 values

\[%~increase = \frac{84.5 - 65}{65} \times 100\]

then decide which percentage increase is greater... Product A (25%) or product B

Answer 14

the formula is

\[increase = \frac{84.5 - 65}{65} \times 100\]

Answer 15

-15.5?

Answer 16

well it should be a positive

\[increase = \frac{19.5}{65} \times 100\]

Answer 17

30?

Answer 18

that makes sense

so whch has the larger increase product A (25%) or product b (30%)

Answer 19

product b?

Answer 20

yes

jobe done

Answer 21

so the answer for part B: ITS: PRODUCT B HAS THE LARGER INCREASE?

Answer 22

right?

Answer 23

correct

Answer 24

thank you so much!!!! can you help me with 2 more or one more please!!!

Answer 25

sorry I can't I'm in Australia and about to go to class

Answer 26

alright its fine, thanks again!