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
<h2>The relationship represents an exponential equation</h2><h2>f(x)=500(1.1)^x</h2>
