Heather has the equation y = 2·3x + 1. she wants to graph a function that represents exponential decay. what should she change in her equation? a) change the 2 to a 1 2 b) change the 3 to a 1 3 c) change the + 1 to a - 1 d) change the x to a 2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4