#### Answer

See the details below.

#### Work Step by Step

Since the function $ g(t)=\frac{t}{t+1}$ is continuous on $[0,1]$ and $ g(0)=0\neq g(1)=0.5$ and $0.499$ is between $ g(0)$ and $ g(1)$, then by the Intermediate Value Theorem the function $ g(t)$ takes on the value $0.499$ for some $ t\in (0,1)$.