PLEASE HELP ME This is an FRQ from ap Calculus and I need help answering it.

FRQ 1

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

FRQ 2

Consider the differential equation dy

dx = x(y – 1).

a) On the axes provided, sketch a slope field for the given differential equation at the 8 given points.

b) Let y = f(x) be the particular solution to the given differential equation with the initial condition

f(1) = 2. Write an equation for the line tangent to the graph of y = f(x) at x = 1. Use your equation

to approximate f(1.5).

c) Find the particular solution y = f(x) to the given differential equation with the initial condition

f(1) = 2.