The table contains some points on the graph of an exponential function. 6
9
1
135
20.25
30.375
4
Determine the a and b values and formulate a model exponential equation to
represent the data in the table. Based on the table, which value of a and b and which
function represent the same relationship?

i think is g(1)=-1.

hope that i can

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.