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.

Acarpool service has 2,000 daily riders. a one-way ticket costs $5.00. the service estimates that for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation. let x represent the number of $1.00 increases in ticket price. choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. then, use the inequality to select all the correct statements. the maximum profit the company can make is $4,125.00. the maximum profit the company can make is $15,625.00. the price of a one-way ticket that will maximize revenue is $12.50. the price of a one-way ticket that will maximize revenue is $7.50.