At the beginning of 2010, a landfill contained 1400 tons of solid waste. The increasing function $W$ models the total amount of solid waste stored at the landfill. Planners estimate that $W$ will satisfy the differential equation $\frac { d W } { d t } = \frac { 1 } { 25 } ( W - 300 )$ for the next 20 years. $W$ is measured in tons, and $t$ is measured in years from the start of 2010. (a) Use the line tangent to the graph of $W$ at $t = 0$ to approximate the amount of solid waste that the landfill contains at the end of the first 3 months of 2010 (time $t = \frac { 1 } { 4 }$ ). (b) Find $\frac { d ^ { 2 } W } { d t ^ { 2 } }$ in terms of $W$. Use $\frac { d ^ { 2 } W } { d t ^ { 2 } }$ to determine whether your answer in part (a) is an underestimate or an overestimate of the amount of solid waste that the landfill contains at time $t = \frac { 1 } { 4 }$. (c) Find the particular solution $W = W ( t )$ to the differential equation $\frac { d W } { d t } = \frac { 1 } { 25 } ( W - 300 )$ with initial condition $W ( 0 ) = 1400$.