Question

For Exercises 3 6, tell whether the relationship between x and y is linear,inverse, exponential, or neither, and explain your answer. If the relationship islinear, inverse, or exponential, write an equation for the relationship. Need help Question 4 only

Answer 1

Problem N 4

step 1

Verify if the relationship is linear

Calculate the slope between two points

we take

(0,500) and (1,550)

m=(550-500)/(1-0)

m=50

Find out the linear equation

y=mx+b

we have

m=50

b=500 ----> Note that the y-intercept is given in the table

so

y=50x+500

Verify if the other points in the table, satisfy the linear equation

For x=2

y=50(2)+500

y=600 -----> In the table the value of y=605

that means

Is not a linear relationship

step 2

Verify if the relationship is inverse

the equation is of the form

y*x=k

where

k is a constant of proportionality

we take the point

(0,500)

y*x=k

500*0=0 -----> k=0

For the point (1,550)

1*550=550 -----> k=550

The relationship is not an inverse relation (because the values of k are different)

step 3

Verify if the relationship is an exponential relation

y=a(b)^x

For x=0, y=500

so

a=500

y=500(b)^x

For x=1, y=550

substitute

550=500(b)^1

550=500b

b=550/500

b=1.1

therefore

y=500(1.1)^x

Verify if the other points in the table, satisfy the exponential equation

For x=2

y=500(1.1)^2=605 -----> is ok

For x=3

y=500(1.1)^3=665.50 ----> is ok

For x=4

y=500(1.1)^4=732.05 -----> is ok

For x=5

y=500(1.1)^5=805.255 ----> is ok

that means

The relationship represents an exponential equation

f(x)=500(1.1)^x