Question

The flight paths of two Thunderbird jets are plotted on a Cartesian coordinate plane, and the
equations of the jets’ flight paths are represented by y=3^x+2 and y = (1/4)^x. Where do the flight paths intersect?

Answer 1

3^x+2 = (1/4)^x
very nasty, what method of solving do you have?
The way you typed the equation, they do not intersect for positive values of x and y
http://www.wolframalpha.com/input/?i=plot+y%3D3%5Ex%2B2+,+y+%3D+(1%2F4)%5Ex

did you mean:
3^(x+2) = (1/4)^x ?? If so, then

log (3^(x+2)) = log ( (1/4)^x )
(x+2)log3 = xlog .25
x log3 + 2log3 = xlog.25
xlog3 - xlog.25 = -2log3
x(log3 - log.25) = -2log3
x = -.884228..
y = 3.4068
see: http://www.wolframalpha.com/input/?i=solve+y%3D3%5E(x%2B2)+,+y+%3D+(1%2F4)%5Ex