Suppose That the Function P(t)satisfies the Differential Equation $P ^ { \prime } ( t ) = P ( t ) ( 4 - P ( t ) )$

True/False

Suppose that the function P(t)satisfies the differential equation $P ^ { \prime } ( t ) = P ( t ) ( 4 - P ( t ) )$ with the initial condition P(0)= 1.Consider the behavior of the graph of $P ( t )$ near a point $t _ { 0 }$ , where $P \left( t _ { 0 } \right) = 4$ (if such a point exists).Is the following graph consistent with P(t)?