Chapter 5 - Exponential and Logarithmic Functions - 5.2 One-to-One Functions; Inverse Functions - 5.2 Assess Your Understanding - Page 268: 98

a)$l(T)=T^2\frac{32.2}{4\pi^2}$ b)$7.38$

a)Here I express $l$ from the function: $T(l)=2\pi\sqrt{\frac{l}{32.2}}\\T^2=4\pi^2\frac{l}{32.2}\\T^2\frac{32.2}{4\pi^2}=l$ b) From part a): $l(T)=T^2\frac{32.2}{4\pi^2}$. Hence plug in $T=3$ to get: $l(3)=3^2\frac{32.2}{4\pi^2}\approx7.38$