## anonymous one year ago (FAN AND MEDAL)

1. anonymous

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)

2. anonymous

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

3. anonymous

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

4. anonymous

@chrisga

5. anonymous

6. campbell_st

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..?

7. anonymous

i need to solve that ?

8. anonymous

90?

9. campbell_st

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

10. anonymous

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

11. anonymous

?

12. anonymous

and for part B?

13. campbell_st

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

14. campbell_st

the formula is $increase = \frac{84.5 - 65}{65} \times 100$

15. anonymous

-15.5?

16. campbell_st

well it should be a positive $increase = \frac{19.5}{65} \times 100$

17. anonymous

30?

18. campbell_st

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

19. anonymous

product b?

20. campbell_st

yes jobe done

21. anonymous

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

22. anonymous

right?

23. campbell_st

correct

24. anonymous

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

25. campbell_st

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

26. anonymous

alright its fine, thanks again!

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