Introduction to Mathematica 101 Supply & Demand Pre Calculus Questions

Do all of your work in Mathematica.

Submit your project as a notebook file (.nb).

For example use Plot, Maximize, Minimize, Reduce, nothing fancy that 101 Mathematica

Comments (* *). write comments to explain the syntax and your steps

1. Suppose that the quantity supplied S and the quantity demanded D for the price p
of t-shirts are given by the following functions:
=
S(p)
D(p)
– 200 + 30p
600 – 20p
=
(a) Define functions for supply and demand. Use these functions for the following
steps.
(b) Plot the supply and demand functions on the same plot.
(c) Find the equilibrium price, and the number of units sold at this price.
(d) Determine the prices for which the demand is greater than the supply.
2. For the function f(x) = –2×2 + 2x + 12
(a) Plot the quadratic function.
(b) Find the zeros.
(c) Find the vertex.
Name:
Math 105
3. The blood pressure (P) of an individual after t seconds with a heart rate of 70
beats/min. can be modeled by the function,
P(t) = 100 + 20 sin
(
77
t
3
(a) Plot two periods of the function.
(b) Find the maximum and minimum values (corresponding to the systolic and
diastolic blood pressure)
(c) In the time interval from Os to ls, determine the times at which the blood
pressure is 100 mmHg.
4. Solve the equation on the interval ( < 0 < 27 2 cos? 0 – 7 cos 0 – 4= 0