How do you find the exponential model #y=ae^(bx)# that goes through the points (-3,2)(1,164)?

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Answer 1 · 2017-02-16T15:55:19

Exponential model is #y=54.5e^(1.10168x)#

As #y=ae^(bx)# goes through #(-3,2)#,

we have #2=ae^(-3b)# ......................(1)

and as #y=ae^(bx)# also goes through #(1,164)#,

we have #164=ae^b# ......................(2)

Dividing (2) by (1), we get

#e^b/e^(-3b)=164/2=82# or #e^(4b)=82# and #4b=ln82=4.40672#

and #b=4.40672/4=1.10168#

Putting this value of #b# in (2), we get

#ae^1.10188=164# or #3.0092a=164#

and #a=164/3.0092=54.5#

and hence exponential model is #y=54.5e^(1.10168x)#