How do you determine the formula for the graph of an exponential function given (0,3) and (2,6)?

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Answer 1 · 2018-04-05T21:22:02

#y = 3e^(ln(sqrt2)x)#

One form of an exponential function is:

#y = y_0e^(kx)" [1]"#

Substitute the point #(0,3)# into equation [1]:

#3 = y_0e^(k0)#

#3 = y_0(1)#

#y_0 = 3 " [2]"#

Substitute equation [2] into equation [1]:

#y = 3e^(kx)" [1.1]"#

Substitute the point #(2,6)# into equation [1.1]:

#6 = 3e^(k(2))#

#2 = e^(2k)#

#ln(2) = 2k#

#k = 1/2ln(2)#

#k = ln(sqrt2)" [3]"#

Substitute equation [3] into equation [1.1]:

#y = 3e^(ln(sqrt2)x)#