The author of this interesting paper studies the life span \(T^*(\lambda,\Phi)\) of the positive, bounded solution \(u(x,t)\) to the Cauchy problem for the nonlinear reaction diffusion equation \(u_t=\Delta u+a(x)u^p\) \((x\in\mathbb{R}^d\), \(t\in(0,T)\), \(p>1)\) under initial condition \(u(x,0)= \lambda \Phi(x)\), where \(\lambda>0\), \(0\leq a\in C^\alpha (\mathbb{R}^d)\), \(0\leq\Phi\in C_b(\mathbb{R}^d)\). The initial function has the property \(\Phi(x)\leq\delta \exp[-\gamma| x|^2]\) \((\delta,\gamma>0)\) or it is bounded. The asymptotic behavior of \(T^*(\lambda,\Phi)\) as \(\lambda\to 0\) in the case that \(T^*(\lambda, \Phi)<\infty\), for all \(\lambda>0\) and as \(\lambda\to\infty\) in all cases is studied accurately. The asymptotic order depends on \(a,\Phi,p\) and \(d\) in case that \(\lambda\to 0\), while on the other hand in the case that \(\lambda\to \infty\), it depends only on whether there is a point \(x_0\) such that \(a(x_0)\), \(\Phi\neq 0\), or whether the supports of \(a\) and \(\Phi\) are separated by a positive distance.