How do you find the equation of the exponential function #y=a(b)^x# which goes through the points(2, 18) and (6,91.125). What is the intercepts of this function?

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Answer 1 · 2017-02-20T05:52:53

#y=8(5/4)^x#
intercept: #(0;8)#

It's
#a*b^2=18# and #a* b^6=91.125# and #b>0#

then

#a=18/b^2# and #18/b^2*b^6=91.125#

#a=18/b^2# and #18*b^4=91.125#

#a=18/b^2# and #b^4=91.125/18=5.0625#

#a=18/b^2# and #b^2=2.25#

#a=18/2.25# and #b=1.25#

#a=8# and #b=5/4#

Then #y=8(5/4)^x#

If #x=0#, then #y=8*(5/4)^0=8*1=8#

It's the one intercept of the function since #y=0 AAx#
graph{8*(5/4)^x [-10, 5, -1, 15]}