Part II: Solving Inequalities Your company needs to temporarily hire a programme
ID: 3104215 • Letter: P
Question
Part II: Solving InequalitiesYour company needs to temporarily hire a programmer to work on a project. Two proposed payment schemes for this work are as follows:
(1) A flat fee of $1,000, plus $20 per hour or (2) $25 per hour.
For each of the two plans, show an expression that can be used to compute the amount of pay for that plan. The variable should be the number of hours worked.
Set up and solve an inequality that would enable your company to determine possible job lengths (in hours) for which the person is paid less according to plan 1 than for plan 2.
Interpret the solution of the inequality in terms of which is better for your company.
Part III: Functions and Graphing
From Part II, express each of the two pay plans as a function of the number of hours worked (again, the variable represent the number of hours.Graph both functions.
Notice in the graph where one function is higher than the other, and interpret this in terms of which pay plan costs the company more (compared to the other plan) for certain numbers of hours worked.
Part IV: Using Exponential Functions
Investing is an important topic for individuals in all areas. Suppose you wish to invest $10,000 in a money market account that earns 4% interest compounded annually. How much would the investment be worth after 10 years? Show all calculations.
Now, suppose that the above investment earns interest compounded quarterly. How much would the same investment be worth after 10 years? Why does the result differ from the previous one?
Part V: Logarithms
One important application of logarithms is found in various computer search routines. For example, a binary search algorithm on a table (or array) of data takes a maximum of log2n (“log base 2, of n”) steps to complete, where n is the number of data elements that can be searched. How many steps (at most) are needed for a search of a table with 16 elements? 512 elements? Explain.
The approximation of the natural logarithm of 2: ln 2 ˜ 0.693 is commonly used by applied scientists, biologists, chemists, and computer scientists. For example, chemists use it to compute the half-life of decaying substances. Based on this approximation and the power rule for logarithmic expressions, how could you approximate ln 8, without a calculator? Explain.