In 2000, there were about 212 million vehicles and about 281 million people in a certain country. The number of vehicles has been growing at 3.5% a year, while the population h growing at 1% a year. (a) Write a formula for the number of vehicles (in millions) as a function of t, the number of years since 2000. Use the general exponential form. V(t) = (b) Write a formula for the number of people (in millions) as a function of t, the number of years since 2000. Use the general exponential form. P(t) = (c) If the growth rates remain constant, when is there, on average, one vehicle per person? Give your answer in exact form and decimal form. Exact form: years since 2000 Decimal form (nearest tenth): years since 2000

A tortoise and hare are competing in a 400-meter race. The arrogant hare gives the tortoise a 220-meter head start. When the start gun is fired, the hare begins running at a constant speed of 3.5 meters per second and the tortoise begins crawling at constant speed of 1.5 meters per second. Take out a piece of paper and read the above problem context again. You will prepare your written work and solutions on your own paper and upload it and the end of this question. Complete the problem solving process by: i. reading and re-reading the problem to identify the quantities in the situation; ii. making a drawing to represent the relevant quantities in the situation; iii. and defining the variable t to represent the number of seconds since the start of the race. a. Define a function f to determine the distance of the tortoise from the finish line in terms of the number of seconds, t, since the start of the race. Preview Solve f(t) = 0 and describe what your solution represents. t = Preview…

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 72 students, requires 5 chaperones, and costs $1,400 to rent. Each van can transport 8 students, requires 1 chaperone, and costs $120 to rent. Since there are 432 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 432 students. Since only 50 parents have volunteered to serve as chaperones, the officers must plan to use at most 50 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs? The officers should rent buses and The minimal transportation costs are $ vans to minimize the transportation costs.

Ms. Cooper wishes to attend a conference which would take place in Hotel Mariott or Hotel Hilton. She isnot sure where the conference will take place but has to make her decision to book a room, immediately.The one-way taxi charges to and from the airport to both hotels are $50. The rooms in Hotel Mariott cost$150 per night and those in Hilton cost $100 per night. The taxi charge from Hotel Mariott to Hotel Hiltonand vice-versa is $20. She needs to book a room for two nights. If she stays in the wrong hotel, she needsto take a taxi from the hotel she is staying to the conference venue and back on days 1 and 2 and take a taxione way on day 3.a) Write the Loss Matrix.b)  What should the probability of conference being conducted at Mariott be so that it does not matter where she stays?

5. Abdi and Brodi are upgrading the storage shed in their backyard. The existing shed has the shape of a rectangular prism with dimensions 1 m by 2 m by 4 m. By what amount should they increase each dimension so that the new shed is 9 times the volume of the original shed? Provide a full algebraic solution.

UUnais, Uid JESSICA pay TO Tem eacII IIOVIE! 2.25 2 Stefanie bought a package of pencils for $1 .75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax. Exactly how many erasers did Stefanie buy?

a) If a Burger plus 2 portion of fries cost $17.00 and 3 Burgers and 4 portion of fries cost $39.00, what is the cost of each item ( Burger and Fries)?

Compute the Laplace Transform of the following differential equations dy(t) (a) 3- + 3y(t) = u(t) dt dy(t) + 10y(t) = 5u(t) dt dt

Luke Thorndike, founder and current president of Thorndike Sports Equipment, had guided the business through 34 successful years and was now interested in bringing his favorite grandson Ted into the company. The elder Thorndike, possessed of a sharp but fading wit, begins the meeting with, “Great to see you, Ted. You always were a high-strung kid. Thought you might like to join our tennis racquet division.” Ted counters, “Not quite, but you’re getting warm, Luke.” The Thorndikes have always been a strange bunch. “Seriously, Ted, I’m getting a little up in years, the microcomputer I bought myself for Christ- mas is collecting dust, and I think you and your business degree could bring some new blood to the company. I’d like you to be my executive vice president. I’ve been running this outfit by the seat of my pants for a lot of years now, and the world just seems to be getting too big and too complicated these days. I’ve got index cards and file folders just about piled up to the ceiling…