Question

HI i need help plz....

#1 the table shows
X F(x)
0 1
1 3
2 9
3 27

Jacqueline claims that the ordered pairs shown in the table are from a linear function.

State if Jacqueline is correct. Explain your reasoning. If you stated Jacqueline is incorrect, be sure to include the type of nonlinear function demonstrated in the table and how you determined your answer.

#2
Kaleigh owns an appliance store. She purchases a new refrigerator to use in her store. The refrigerator depreciates by a fixed rate per year. The function V = 2,600(0.74)t can be used to model the value of the refrigerator after t years.

Part A: Explain what the parameter 2,600 represents in the equation of the function.

Part B: By what percentage does the value of the refrigerator increase or decrease each year? Explain your answer.

Part C: What is the value of the refrigerator after 3 years rounded to the nearest dollar? You must show your work.

Answer 1

Ques 1: Jacqueline is correct as the function is
`y=3x+1`.

Ques 2: A - 2600 is the initial value of the refrigerator in dollars.

B - Value of the refrigerator increases by 26%

C - Value of the refrigerator after 3 years is $1066.

Explanation:

Ques 1: From the table, we have the ordered pairs (0,1) and (1,3).

The slope of the line is given by
`(3-1)/(1-0)` = 3

So, we have the equation of the straight line as,
`y=3x+b`.

Substituting, (0,1) in the equation, we get,

`1=3* 0+b` i.e. b= 1

Thus, the equation of the function is,
`y=3x+1`, which is a linear function.

It can be easily verified that all the points satisfy the equation.

Hence, Jacqueline is correct.

Ques 2: We are given the function as,
`V = 2,600(0.74)^t`

Part A - Substituting t = 0 in the function, we get,

`V = 2,600(0.74)^0` i.e. V= $2600

That is, 2600 is the initial value of the refrigerator in dollars.

Part B - Since the function is,

`V = 2,600(0.74)^t`

i.e.
`V = 2,600(1+0.26)^t`

That is the value of the refrigerator increases by 0.26 rate or 26%.

Part B - We have the function for the value of refrigerator as,
`V = 2,600(0.74)^t`

So, after 3 years, the value is,

`V = 2,600(0.74)^3`

i.e.
`V = 2,600* 0.41`

i.e. V = $1066

Thus, the value of the refrigerator after 3 years is $1066.