Question

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

a) 2/5
b) 4/9
c) 5/8
d) 3/4
e) 5/4

Answer 1

Answer will be a fraction, so write 6.25 as a fraction: 25/4
\[r^t = \frac{25}{4}r^{t+2}\]Divide both sides by \(r^t\)
\[1 = \frac{25}{4}r^2\]Take square root of both sides\[1 = \sqrt{\frac{25}{4}}*\sqrt{r^2}\]Simplify and solve for \(r\)