How do you find the exponential model #y=ae^(bx)# that goes through the points (5,3200) and (11,6800)?

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Answer 1 · 2016-09-02T10:45:53

#y=3200(17/8)^((x-5)/6)#.

Let us denote, by #C#, the curve # ; y=ae^(bx)#.

#C# passes thro. the pts. #(5,3200) and (11,6800)#, hence, the co-ords. of these pts. must satisfy the eq. of #C#.

#:. 3200=ae^(5b)......(1), and, 6800=ae^(11b)......(2)#

#(2)-:(1)" gives, "6800/3200=(ae^(11b))/(ae^(5b))#

#rArr 17/8=e^(6b) rArr (17/8)^(1/6)=e^b#

Then, by #(1), a=3200/(e^b)^5=3200/(17/8)^(5/6)=(8/17)^(5/6)3200#

Hence, the reqd. expo. model is # : y=(8/17)^(5/6)3200(17/8)^(x/6)#,

#=3200(17/8)^(x/6)*(17/8)^(-5/6#, i.e.,

#y=3200(17/8)^((x-5)/6)#.

Enjoy maths.!