In the following exercises and problems you will be able to apply models of situations related to business administration using linear, polynomial, exponential and logarithmic functions. Correctly use mathematical notation or terminology. Make sure to include correct mathematical procedures and provide clear and complete explanations and interpretations. Remember to express the solution in the context of the situation.

Note: In the case that the result is decimal, you will round it to two decimal places.

1. A company provides its representatives with a car for their official use in the company. The company must determine whether to buy or rent the car they will use. The company has the following options:

? Buy the car with a down payment of $ 50,000, plus 24 fixed monthly payments of $ 3,500 that include insurance. At the end of the 24 months, the car can be sold for $ 59,400.

? Rent a car for $ 2,200 per month plus $ 0.15 per mile traveled and a one-time payment of $ 7,500 for auto insurance for two years.

The company estimates the average of its trips per month will be 850 miles per month for the next two years. Which option is the most convenient for the company in terms of lower costs?

2.The number of units sold weekly of a certain product depends on the amount x in dollars invested in advertising and is given by the function y = 70 + 150x - 0.3x². How much should you spend a week on advertising to get maximum sales volume?

3. An employer pays $ 3,000 monthly rent for office space and $ 1,000 to 12 employees, plus a bonus of $ 10 for each work unit completed by the employee during the month. In addition, the employer has a profit of $ 18 per unit of work per employee.

Suppose an employee completes 300 units in one month. Also suppose that all employees completed 300 units. Calculate the employer's income.

4. The y value of a car (in thousands of dollars) can be approximated using the model y = 25(0.85)^t, where t is the number of years since the car was new.

Indicate whether the model represents exponential growth or decay. Justify your answer.

1. If P dollars are invested at the end of each year in an annuity that bears interest at an annual rate r, the amount in the account will be A dollars after n years, where

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