How do you write an exponential function whose graph passes through the points (0,3) and (-1,6)?

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Answer 1 · 2016-11-17T18:27:27

Please see the explanation.

Given: #(0, 3) and (-1, 6)#

Using the equation:

#y = ae^(alpha(x))#

Substitute 0 for x and 3 or y:

#3 = ae^(alpha(0))#

#a = 3#

Substitute 3 for a:

#y = 3e^(alpha(x))#

Substitute -1 for x and 6 for y:

#6 = 3e^(alpha(-1))#

Divide by 3

#2 = e^(alpha(-1))#

Natural log of both sides:

#ln(2) = -alpha#

#alpha = ln(1/2)#

Substitute #ln(1/2)# for #alpha#:

#y = 3e^(ln(1/2)(x))#

Here is the graph:

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