Answer
$R=791 ft$
Work Step by Step
We are using the formula $R=\frac{V^{2}}{g(f+\tan\theta)}$ where R is the safe radius of the curve, V is the velocity in feet per second, $\theta$ is the superelevation and $f$ and $g$ are constants to calculate the radius of the curve.
In this case taking the values from Exercise 77 with the new velocity $V=70mph$,
$\theta=3^{\circ}$
$g=32.2$
$f=0.14$
Converting the miles per hour to feet per second, with the hint from Exercise 77: $45mph=66ft/s$
$V=70mph*\frac{66ft/s}{45mph}=102.7ft/s$
Substituting in the formula,
$R=\frac{102.7^{2}}{32.2(0.14+\tan(3^{\circ}))}$
$R=1702ft$ (rounded to the nearest feet)
