Match the following items. 1. a function in the form of y = ax
natural logarithm
2. "x" in the exponential form y = ax
logarithms
3. a logarithm with a natural base of e
exponent
4. rectangular arrangement used to organize data
exponential function
5. "a" in the exponential form y = ax
common logarithm
6. a logarithm with a natural base of 10
base number
7. equivalent form of an exponential function
matrix

step-by-step explanation:

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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.