Question

If r> 0 and r^t = 6.25r^t+2, then r =

Answer 1

I'm going to use n instead of t

rⁿ=6.25rⁿ+2
minus rⁿ both sides
0=5.25rⁿ+2
minus 2 both sides
-2=5.25rⁿ
divide both sides by 5.25
-2/5.25=rⁿ
take the nth root of both sides
$\sqrt[n]{\frac{-2}{5.25}}= \sqrt[n]{r^n}$
$\sqrt[n]{\frac{-2}{5.25}}= r$