The EXPONENTIAL REGRESSION equation obtained by fitting the data is
To obtain the exponential regression equation which models the data, we could use technology, we involves Inputting the data into an EXPONENTIAL REGRESSION CALCULATOR or EXCEL
Using an exponential regression calculator :
The regression equation obtained is :
The general function of an exponential regression function is :
A = 58.031 = Initial value ; B = Decay factor
Hence, the EXPONENTIAL REGRESSION EQUATION obtained using technology is :
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In order for the inverse to exist, the matrix cannot be singular, so we need to first examine the conditions for existence of the inverse.
Compute the determinant. The easiest way might be a cofactor expansion along either the first row or third column; I'll do the first.
The matrix is then singular whenever
.
With this in mind, compute the inverse.
The value of b is the y intercept or when the line crosses the y axis
this only happens when the value of x=0
so just look for the ordered pair in the table with x=0 and y=b
so if you had a table and saw
(0,3)
(x,y)
so the point where x=0 is at point (0,3) y=3
therefor b=3
basically look for the matching y value for when x=0
5.250
To change a fraction to a decimal fraction divide the numerator by the denominator.
that is 21 ÷ 4 = 5.250 ( to 3 decimal places )
The answer is d 1 in = 4m