Study Island. Linear and Exponential Models

Transcription

1 Study Island Copyright 2014 Edmentum - All rights reserved. 1. A company is holding a dinner reception in a hotel ballroom. The graph represents the total cost of the ballroom rental and dinner. 3. In an organism whose environment does not affect cell division, a parent cell divides into two daughter cells. Those two daughter cells each divide into two more cells for a total of four cells in the If those four cells each divide into two more cells, there will be eight cells in the If each of these cells continue to divide in the same manner, how many cells will be in the organism after fourteen divisions? A. 268,435,456 B. 8,192 C. 16,384 D Which function family would be used to solve the following question? Which function represents the data displayed in the graph? f(x) = $7.50x + $ A. f(x) = $625.00x + $7.50 B. f(x) = $0.75x + $ C. f(x) = $625.00x + $0.75 D. 2. The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below. C = $3,173 + $31u If the company wants to keep the cost of operation under $6,000 per month, what is the maximum number of units they can produce? A. 91 B. 92 C. 910 D. 911 A rabbit population doubles every year. If the rabbit population starts with 5 rabbits, then how many will there be in 6 years? A. Absolute Value Function Family B. Quadratic Function Family C. Exponential Function Family D. Linear Function Family 5. A pan is heated to 433 F, then removed from the heat and allowed to cool in a kitchen where the room temperature is a constant 71 F. The formula below can be used to find D, the difference in temperature between the pan and the room after t minutes. D = 362e -0.03t What is the approximate temperature of the pan after it has been away from the heat for 20 minutes? A F B F C F D F

2 6. A contract delivery worker is paid $12.00 per hour as well as $0.50 per mile. Assuming a 40-hour work week, which of the following equations below gives the amount of money per week that the worker makes before taxes, M, as a function of the number of miles, m, driven during the week? 9. The graph below represents the bacteria population after t minutes. A. M = m B. M = 12.5m C. M = m D. M = m 7. A car was originally purchased for $25,000. The following equation gives the car's value when it has been driven a total of m thousand miles over a period of t years. If the car has been driven a total of 25,000 miles over a period of 7 years, what is its value? A. $3, B. $1, C. $7, D. $3, The table below represents a linear situation. x f(x) Use this table to construct the function that it represents. A. f(x) = -3x - 4 B. f(x) = -4x - 3 C. f(x) = -4x - 23 D. f(x) = 4x + 15 Construct the function which represents the data displayed in the graph. A. P(t) = 200(2) t B. P(t) = 50(4) t C. P(t) = 50(2) t D. P(t) = 4 t In order to pay back a debt, Mark has set up a bank account. He has asked that 11% of the total amount in the account be withdrawn each month as a payment towards his debt. If Mark started the account with $8,961.00, and has not made any further deposits, what will the approximate balance in the bank account be after 14 months? (Hint: Use the formula for depreciation, y = A(1 - r) t, where A is the initial amount in the account, r is the withdrawal rate in percentage terms, and t is the amount of time that has passed in months.) A. $1, B. $7, C. $1, D. $1, Answers

3 1. A 2. A 3. C 4. C 5. D 6. D 7. D 8. B 9. B 10. C Explanations 1. The graph is a linear function represented by an equation of the form f(x) = mx + b, where m is the rate of change and b is the initial value. First, calculate the rate of change, or slope, between any two points on the graph. In this case, use the points (10, 700) and (30, 850). under $6,000 and a fraction of a unit cannot be made, the maximum number of units they can produce is After zero cell divisions, there is one cell in the 1 = 2 0 After one cell division, there are two cells in the 2 = 2 1 After two cell divisions, there are four cells in the 4 = 2 2 After three cell divisions, there are eight cells in the 8 = 2 3 After x cell divisions, the number of cells in the organism can be represented by the following equation. f(x) = 2 x Next, determine the initial value. The initial value is the value of f(x) when x equals 0. According to the graph, the initial value is $625.00, which is the rental fee for the ballroom. Therefore, the function that represents the graph is f(x) = $7.50x + $ To determine the maximum number of units, substitute $6,000 in for C in the given equation, and then solve for u. $6,000 = $3,173 + $31u $2,827 = $31u u Since the company wants their operating cost to be Therefore, after fourteen cell divisions, there will be 2 14 = 16,384 cells in the 4. Growth that doubles every year is always modeled by an exponential function. Since the problem states that the rabbit population doubles every year, then an equation in the exponential function family would be used to solve this question. 5. First, substitute t = 20 into the formula and solve for D. D = 362e -0.03(20) D F Next, since D is the difference between the temperatures of the pan and of the room, add D to

4 the temperature of the room to find the temperature of the pan. 71 F F = F 6. First, calculate the amount of money the worker will make given a 40-hour work week at $12.00 per hour. (40)($12.00) = $ Then, add this to the amount of money that the worker will get paid per mile to get the total weekly earnings. $ $0.50m Therefore, the equation that gives the amount of money per week that the worker makes before taxes, M, assuming a 40-hour work week as a function of the number of miles, m, driven during the week is given below. M = m 7. First, decide what the variables m and t are equal to. Since the car has been driven 25,000 miles, m = 25. Since the car has been driven for 7 years, t = 7. Next, substitute these values into the given equation, and then use the order of operations to solve for V (-27) = -4 So, the slope is -4. The y-intercept occurs at the point where x is zero. The table does not show an x-value of zero. Instead, use the point-slope form of a line, shown below, where (x 1, y 1 ) represents a point on the line, and m represents the slope. (y - y 1 ) = m(x - x 1 ) Substitute the point (4, -19) and the slope, -4, into the equation. Then, transform the equation so that it is in slope-intercept form. (y - (-19)) = -4(x - 4) y + 19 = -4x + 16 y = -4x y = -4x - 3 Therefore, the function f(x) = -4x - 3 represents the linear situation in the table. 9. Exponential functions are of the form f(x) = a(b) x, where b is greater than zero and not equal to one. Calculate the common ratio. The calculations below use the points (0, 50), (0.5, 100), (1, 200), (1.5, 400), (2, 800), and (2.5, 1,600). The change in the t-values is 0.5, so divide 2 by A linear function can be represented by an equation in slope-intercept form, shown below, where m represents the slope, and b represents the y-intercept. f(x) = mx + b First, determine the slope of the line. Notice that the x-values increase by 1. The difference between the f(x)-values will reveal the slope (-19) = (-23) = -4 So, the common ratio is 4. Thus, the exponential function will have the form P(t) = a(4) t. Use the point (0, 50) to find the value of a. Therefore, the function that represents the data in the graph is P(t) = 50(4) t.

5 10. Evaluate the depreciation formula with the given values of A, r, and t. Therefore, after 14 months, the approximate balance of the bank account will be $1,