4 math problems

(i need steps)


1.During the first couple weeks of a new flu outbreak, the disease spreads according to the equation I(t)=5400e^0.076t, where I(t) is the number of infected people t days after the outbreak was first identified.

Find the rate at which the infected population is growing after 8 days and select the appropriate units.

2.At a price of x dollars, the supply function for a music player is q=65e^0.004x, where q is in thousands of units.

How many music players will be supplied at a price of 275? (Round to the nearest thousand.)
________thousand units

Find the marginal supply
Marginal supply(x) = _______

Which is the best interpretation of the derivative?
The rate of change of the quantity supplied as the price increases
The rate of change of the price as the quantity supplied increases
The quantity supplied if the price increases
The price at a given supply of units
The number of units that will be demanded at a given price


3. For some tasks, a sigmoid learning curve is used to model proficiency. Suppose the percent proficiency is given by the model P(t)=100/(1+60e^−0.6t), where t is days of practice.

Find the inflection point, the point where additional practice starts producing diminishing returns. Give your answer accurate to at least 2 decimal places.

_______days


4.The concentration of a drug t hours after being injected is given by C(t)=0.2t/(t^(2)+59). Find the time when the concentration is at a maximum. Give your answer accurate to at least 2 decimal places.

_________hours