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) = 0.69(1.03)^x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? please 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) 10,100 10,201 10,303.01 10,406.04

Answer 1

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

Answer 2

please help!!!

Answer 3

@mathmale

Answer 4

for B, take the price of year 2 - the price of year 1, you get
10,201 - 10,100=101
then take the price of year 3- the price of year 2, you get
10,303.01-10201=102.01 (a little bit up, right?)
do the same with year 4, 3
10,406.04-10,303.01=103.03 (a little bit up again, right?)

Answer 5

so the price of product B increases year after year that allows me make the conclusion as above

Answer 6

Thank you so much... can you please help me with 2 more or is that asking to much???

Answer 7

I'm new

Answer 8

umm idk i guess

Answer 9

How do I medal more than once??? :-)

Answer 10

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


Number of years 1 2 3
Option 1 (amount in dollars) 1300 1690 2197
Option 2 (amount in dollars) 1300 1600 1900


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. (2 points)

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)

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. (4 points)

Answer 11

A: linear; exponential. The change between years is constant for option 1 and not for option 2.

Answer 12

B: https://tex.z-dn.net/?f=100x%2B1000%5C%5C5.5x%5E2%2B93.5x%2B1001

Answer 13

C: https://tex.z-dn.net/?f=100%2820%29%2B1000%5C%5C2000%2B1000%5C%5C3000%5C%5C%5C%5C5.5%2820%29%5E2%2B93.5%2820%29%2B1001%5C%5C5.5%28400%29%2B1870%2B1001%5C%5C2200%2B2871%5C%5C4871

Answer 14

Yes; 4871 is significantly greater than 3000

Answer 15

Do the links just say what the answer is?

Answer 16

umm no i cant really tell the the direct because mathmale gonna tell me something agine

Answer 17

Ok, but what can I do with said numbers?

Answer 18

@wanell

Answer 19

? said numbers ?

Answer 20

in the links

Answer 21

ok let me go over this

Answer 22

Number of years 1 2 3
Option 1 (amount in dollars) 1300, 1690, 2197
Option 2 (amount in dollars) 1300, 1600, 1900) is that right

Answer 23

option 1 is exponential because it changes by a factor of 1.3 each year
option 2 is linear because it increases by a fixed amount each year, here 300 .

Answer 24

part b) is to find the linear and exponential functions

Answer 25

for part b)

Option 1:
Directions: Fit data to exponential model f(n) = a * b^n
if you divide 1300 by 1.3 , you will get 1000. Therefore
n=0 , f(0) = 1000
so the exponential function is
f(n) = 1000 * (1.3)^n

Option 2:
Directions: Fit data to a linear model f(n) = m*n + b
if you calculate slope you get m = 300
and subtract 300 to get
n=0, f(0) = 1000
So the linear model is
f(n) = 300*n + 1000

Answer 26

option 1:

y(x) = A*b^x use 2 points to find, A and b

Answer 27

0,1000) gives

y(0) = 1000 = A*b^0
1000 = A

The function is now

y(x) = 1000 *b^x

Answer 28

(1 , 1300) second point

y(1) = 1300 = 1000*b^1
1300 = 1000b b=1.3

The function is

y(x) = 1000*(1.3)^x

Answer 29

option 2 is a line, starts at y intercept of 1000 investment, and slope of 300 dollars per year

y(x) = 300x + 1000

Answer 30

option1
y(x) = 1000*(1.3)^x

option2
y(x) = 300x + 1000

Graph them, and describe what you see.

Answer 31

part c, look at x=20, and go straight up, which one has a larger y value, it will be the exponential option 1.

Answer 32

sorry for absence had to do something but please clarify @wanell @mathmale