Maths For Finance Questions

2. Find the equilibrium values of p and q in a competitive market where the demand schedule is

p = 200q−1 (-1 is in superscript)
and the supply function is
p = 30+20q

3. A marketing-research company needs to determine how people adapt to the taste of a new cough drop. In one experiment, a person was given a cough drop and was asked periodically to assign a number, on a scale from 0 to 10. to the perceived taste. This number was called the response magnitude. The number 10 was assigned to the initial taste. After conducting the experiment several times, the company estimated that the response magnitude is given by

R = 10e−t/40 (-t/40 is in superscript)

where t is the number of seconds after the person is given the cough drop.

(a) Find the response magnitude after 20 seconds. Give your answer to the nearest integer.

(b) After how many seconds does a person have a response magnitude of 5? Give your answer to the nearest second.