If the relationship is proportional, what is the missing value from the table?
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Answer:
1 is the positive difference in the y-intercept value of f(x) and g(x)
Step-by-step explanation:
The linear function f(x) passes through the points (0, 3) and (2, 7)
Here (0,3) is the point where f(x) crosses y axis
So y intercept = 3
Now we find g(x) from the given table
g(x) is an exponential function
General form of exponential function is g(x)= ab^x
Now we use the given values from the table
When x=2 , g(x)= 18
Plug in the values
=>
(equation 1)
When x=3 , g(x)= 54
Plug in the values
=>
(equation 2)
Divide second equation by first equation
so b = 3
We know 18 = ab^2
Plug in 3 for b
18= 9a
Divide by 9 on both sides
So a= 2
So g(x) becomes
To find y intercept we plug in 0 for x
g(x) = 2(3)^2= 2
So y intercept = 2
y intercept of f(x) is 3 and y intercept of g(x) is 2
Difference is 3-2 = 1