Modelling with Indices 10. A person offers you one of two prizes: Prize (A) $1000 right now. Prize (B) 1 cent doubled every day for 20 days. (a) By simply guessing, which one would you take? (b) Write down the amount for Prize (B) for the first four days: Day 0 Day 1 Day 2 Day 3 | Day 4 1c 2c (c) Do you see a pattern? Create a formula for the amount after n days. (d) Using your formula, how much is Prize (B) worth after the 20 days has elapsed? (You can use a calculator).

Modelling with Indices 10. A person offers you one of two prizes: Prize (A) $1000 right now. Prize (B) 1 cent doubled every day for 20 days. (a) By simply guessing, which one would you take? (b) Write down the amount for Prize (B) for the first four days: Day 0 Day 1 Day 2 Day 3 | Day 4 1c 2c (c) Do you see a pattern? Create a formula for the amount after n days. (d) Using your formula, how much is Prize (B) worth after the 20 days has elapsed? (You can use a calculator).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 20E: Renting Motel Rooms You own a motel with 30 rooms, and you have a pricing structure that encourages...

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Renting Motel Rooms You own a motel with 30 rooms, and you have a pricing structure that encourages rentals of rooms in groups. One room rents for 85, two rent for 83 each, and in general the group rate per room is found by taking 2 off the base of 85 for each extra room rented. a. How much money do you take in if a family rents two rooms? b. Use a formula to give the rate you charge for each room if you rent n rooms to an organization. c. Find a formula for a function R=R(n) that gives the revenue from renting n rooms to a convention hose. d. What is the most money you can make from rental to a single group? How many rooms do you rent?
Finance To expand its clothing line, a small corporation borrowed $775,000 from three different lenders. The money was borrowed at 8,9and10, simple interest. How much was borrowed at each rate when the annual interest owed was $67,500 and the amount borrowed at 8 was four times the amount borrowed at 10 ?
Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.
Forensics At 8:30 A.M., a coroner went to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person’s temperature twice. At 9:00 A.M. the temperature was 85.7F, and at 11:00 A.M. the temperature was 82.8F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula t=10lnT7098.670 where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person’s body. (This formula comes from a general cooling principle called Newton’s Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6F at death and that the room temperature was a constant 70F.) Use the formula to estimate the time of death of the person.
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Sales Strategy A small business is considering hiring a new sales representative sales rep to market its product in a nearby city. Two pay scales are under consideration. Pay Scale 1 Pay the sales rep a base yearly salary of 10, 000 plus a commission of 8 of total yearly sales. Pay Scale 2 Pay the sales rep a base yearly salary of 13, 000 plus a commission of 6 of total yearly sales. a. For each of the pay scales above, use a formula to express the total yearly earnings for the sales rep as a function of total yearly sales. Be sure to identify clearly what the letters that you use mean. b. What amount of total yearly sales would result in the same total yearly earnings for the sales rep no matter which of the two pay scales is used? c. On the same screen, plot the graphs of the functions you made in part a. Copy the picture onto the paper you turn in. Be sure to label the horizontal and vertical axes, and be sure your picture includes the number you found in part b. d. If you were a sales rep negotiating for the new position, under what conditions would you prefer pay scale 1? Under what conditions would you prefer pay scale 2?
Investments Jack invest $1000 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one half percent higher. If he receives a total of $190 interest in 1 year, at what rate is the $1000 invested?