A company opened a business selling financial magazines. The demand function for financial magazines is given by: .
a) Find quantity demanded () at the price level.
b) Find the derivative of quantity with respect to price ()
c) Find the price elasticity of demand when.
d) Is demand for financial magazines elastic, unit elastic, or inelastic at this price level?
e) Would an increase in price lead to an increase in revenue for the company?
a) Consider the following quadratic equation:
i) Find the derivative of y with respect to x; .
ii) Find the turning point of the curve.
iii) Find the gradient at the point where the curve crosses the y-axis.
b) Find the partial derivative with respect to of the following function:
a) Marks awarded on a test for a group of students were normally distributed with a mean of
50
and a standard deviation of
6.
i) What is the z-score for a student that was awarded a mark of
53?
ii) What percentage of students got a mark below
53?
b) A survey of
100
employees found that the average time spent commuting last week was
6
hours with a standard deviation of
4
hours. Conduct a hypothesis test at the
5%
significance level to examine whether the average time spent commuting for all workers is exactly
5
hours or more than
5
hours. Make sure to include in your solution the null and alternative hypotheses, the critical value, the test-statistic value and the decision made.