The Exponential Trendline fits data to the expression

*y = B **´ exp(Ax)* (1)

The LOGEST function fits data to the expression

*y = B **´ M ^{x} * (2)

How can we get the trendline values into a worksheet cell?

Comparing expression (1) and (2) we see that:

*M ^{x}*

Taking natural logarithms of both sides of (4) gives:

*xLn**(**M) = Ax* (4)

From which we see: *A = Ln(M)* (5)

Hence, the natural logarithm of the first term (M) obtained from the LOGEST function equates to the A term in the Trendline expression

In the attached worksheet the data (A5:B14)
was used to make the XY chart. An exponential trendline was added to the chart
giving the expression *y = 3 **´ exp(0.25x)*.

The range G3:H3 was selected and the
formula =LOGEST(B5:B14, A5:A14) was entered and
completed with SHIFT+CTRL+ENTER since it is an array function. We see that this
gave *M* = 1.284 and *B* = 3.00. In I3 the formula =LN(G3) gives the result 0.25 as the value of *A*. This
is in agreement with our expression (5) above.

There are a number of ways of obtaining the predicted y-values. These are shown in column C, D and E.

Alternatively, one may use LINEST to obtain the A and B values in cells – see smaller diagram.

November 2005