Question

Please help mee D: ???

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.

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.

Answer 2

@undeadknight26 @jim_thompson5910

Answer 3

hint: rewrite 1.25 into the form 1+r

Answer 4

so 1+1.25=2.25?

Answer 5

1.25 = 1+r

solve for r

Answer 6

I dont knoww

Answer 7

1/4?

Answer 8

1/4 = 0.25, so yeah

Answer 9

r = 0.25

Answer 10

since r is positive, we have 25% growth

Answer 11

so the inflation rate is 25% (the price increases by 25% each year)

Answer 12

Okay. what about Part B: The table below shows the price f(t), in dollars, of product B after t years:

Answer 13

what's the difference in 65 and 84.5

Answer 14

19.5?

Answer 15

divide that by the first number 65

Answer 16

.30

Answer 17

do the same for 84.5 and 109.85

Answer 18

i got 0 o.o

Answer 19

whoops, i did something wrong

Answer 20

yeah i got .30 again

Answer 21

how about from 109.85 to142.81

Answer 22

.30

Answer 23

so every year, product B is increasing in price by 30%

Answer 24

Thank you C:

can you help with one more?

Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years:

Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331


Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer.

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.

Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option.

Answer 25

how far did you get?

Answer 26

Linear function right? I'm not quite sure what im doing.

Answer 27

why do you think option 1 is linear?

Answer 28

Beacuse they only have a difference of 100?

Answer 29

correct

Answer 30

so every year, the investment in option 1 is growing by $100

Answer 31

Yes.

Answer 32

in the second one, it grows by 110, then 121

Answer 33

so that isn't linear

Answer 34

what is the percentage change from year to year in option 2?

Answer 35

10%?

Answer 36

correct

Answer 37

so that proves it's exponential

Answer 38

For Part
B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.

how would I write the function?

f(n)=...

Answer 39

what is the general form of linear equations?

Answer 40

y = mx + b

Answer 41

m is the slope, ie rate of change

Answer 42

it's how much it's changing each year, so m = ???

Answer 43

m=100

Answer 44

good

Answer 45

x = 1 (year 1)
y = 1100 (amount of money in year 1)


y = mx + b

y = 100x + b ... plug in m = 100

1100 = 100*1 + b ... plug in x = 1, y = 1100

solve for b

Answer 46

b=1000?

Answer 47

yes

Answer 48

so the linear equation is y = 100x + 1000 and replace y with f(n) and x with n to get

f(n) = 100n + 1000

Answer 49

you can now plug in any value of n you want to find out how much money there is for any year n

Answer 50

what about the second option? How would i write a function for that one?

Answer 51

the general equation for exponential growth is

f(n) = P*(1+r)^n

P is the starting value
r is the growth rate
n is the number of years

Answer 52

Would i have to make more than one function?

Answer 53

one function per option

Answer 54

two options ----> two functions

Answer 55

I meant for the second option xDD i dont understand what i'd have to plug in

Answer 56

like...
f(n) = 1100*(1+10%)^1 ??

Answer 57

close

Answer 58

what is the original amount she invested

Answer 59

Ohh, 1000

Answer 60

P = 1000

Answer 61

r = growth rate ---> r = 0.10 (10% = 0.10)

Answer 62

then n =... ? number of years, but what years xD

Answer 63

you leave it as n for now

if you wanted a certain year, say n = 1, you'd plug in n = 1

Answer 64

so the function is

f(n) = 1000(1.10)^n

Answer 65

So, for C i would plug in 20 for n??

Answer 66

plugging in values of n will give you the amounts of money in the account

Answer 67

correct, for each function

Answer 68

then you compare the difference

Answer 69

I think i can do C by myself. I'll give you the answers i come up with and can you check them please? I want to see if i can get it

Answer 70

go ahead

Answer 71

for the first option after 20 years she would get 3,000. For the second option she gets 6,727.5. The difference being 3,727.5. If she uses option two over option one, it would be a better choice because she would be getting the greatest amount in 20 years.

Answer 72

very nice

Answer 73

Thank you for helping me, again c: I like it a lot better how you help me figure things out and you don't just give an answer without explanation.

Answer 74

you're welcome and it's good to go through it like that (instead of just being given the answer)