Evaluate the function below at x=5. Then, enter your solution. f(x)=3(2)^x

Solution: f(5) = 96

Step-by-step explanation:

f(5) = 3(2)^5

f(5) = 3 (2 × 2 × 2 × 2 × 2)

f(5) = 3 (32)

f(5) = 96

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