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A variation of the False Position Method for finding Roots which fits the function in question with an exponential.
See also False Position Method
References
Ostrowski, A. M. Ch. 12 in Solutions of Equations and Systems of Equations, 2nd ed. New York: Academic Press, 1966.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Secant Method, False Position Method,
and Ridders' Method.'' §9.2 in
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, pp. 347-352, 1992.
Ralston, A. and Rabinowitz, P. §8.3 in A First Course in Numerical Analysis, 2nd ed. New York: McGraw-Hill, 1978.
Ridders, C. F. J. ``A New Algorithm for Computing a Single Root of a Real Continuous Function.''
IEEE Trans. Circuits Systems 26, 979-980, 1979.