The spread of a fungal infection in an ant colony can be modeled by dy/dt =(y + 1)/(2√t)
where t is the time in hours and y is the percent of the ants infected. At t = 1 only three percent of the ants are infected.

(a) Write an equation for the line tangent to the graph of y at t = 1. Use the tangent line to approximate the percentage of the colony infected at t = 1.2.

(b) Find y explicitly in terms of t.