Modeling with Systems — Unit test Answers

Which of the following best describes how the y values are changing over each interval?xy122438416532

A customer deposits $500 in an account that pays 4% annual interest. What is the balance after 3 years if the interest is compounded annually?Compound interest formula: t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

Adita has two options for how to invest $1,000.Plan A: Put the $1,000 in an account that pays $100 per year.Plan B: Put the $1,000 in an account that pays 5 percent interest per year.Which statement is true?

A store owner puts in an order for product X and product Y for a total of 4,000 units. It costs $0.10 per item to ship of product X and $0.04 per item to ship product Y. If the total shipping cost is $352, which system of equations can be used to determine how much of product X and product Y the store owner bought?

The scatterplot shows the number of minutes Tyler played in his last eight basketball games and the points he scored in each game. Estimate the location of the line of best fit. About how many points would Tyler score if he played for 40 minutes?

The table below shows the different times it takes Paula to drive to her grandmother’s house depending on the rate at which she drives.Rate vs. TimeRate (mph)30405060Time (h)2.51.8751.51.25If one day Paula rides a scooter to her grandmother’s house at a constant rate of 24 miles per hour, how long should it take her?

Over which interval are the exponential and linear function approximately the same?

Consider a cube with an inscribed sphere. The function can be used to find the radius, r, of a sphere given the volume, V. The function can be used to find the side length of the cube, s, depending on the radius of the sphere. The function can be used to find the surface area, A, of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?

A customer deposits $1,000 in an account in which the interest is compounded annually. The table below shows the balances in the account at the end of each year.Amount in Account vs. Number of YearsAmount in Account, ANumber of Years After Initial Deposit, t1,00001,08011,166.4021,259.7131,360.494Which equation best represents the data in the table?

A car dealership is offering $1,500 cash back on the purchase of a new vehicle. The cost, after the cash back, of a new vehicle can be modeled by the function C(x) = x – 1,500, where x is the original price of the vehicle. The vehicle is subject to a sales tax of 8.43%, so the total price of the vehicle is represented by the function P(C) = 1.0843C.

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

For which scatterplot is the correlation strongest?

A company plans to sell embroidered hats for $15 each. The company’s financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). What is the minimum number of hats the company must sell to make a profit?

Ashley is a member of the Movie-a-Month Club, where she rents movies each month. She uses the table below to keep track of the number of movies she rents each month and the total cost, which includes her monthly membership fee.Number of Movies vs. Total CostNumber of Movies1215922Total Cost$35.00$42.50$27.50$60.00Ashley graphed the relationship in the table. What is the slope of the graph, and what does it represent?

A mortgage company offers a loan for 30 years at an annual rate that is equal to the prime rate published by the Federal Reserve plus 2%. This can be modeled using the function APR(p) = p + 0.02, where p is the prime interest rate as a decimal. The annual interest rate is then converted to a monthly interest rate using the function . The Wilsons want to borrow $128,000. Their monthly payments can be calculated by the function .