Lex D.

asked • 03/06/19

Given the two points (2,3) and (4,27), find the equation of the exponential function that passes through these two points.

need to use the formula y = ab^x

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Paul M. answered • 03/06/19

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3 = Ab2

27 =Ab4


log 3 = log A + 2 log b

3 log 3 = log A + 4 log b


Subtract

2 log 3 = 2 log b

b = 3


log 3 = log A + 2 log 3

log A = -log 3 = log(1/3)

A = 1/3


y = (1/3)*3x = 3x-1


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Paul M.

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“log” is the usual abbreviation for the common (base 10) logarithm. In this case it really doesn’t matter what base log you choose initially because the base 3 comes out by the nature of the problrm.
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03/06/19

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