I need help with the ones that are circled. 159 Linear Functions as Models Secti

Question

I need help with the ones that are circled.

159 Linear Functions as Models Section 4-3 14. The deposits at Money Masters Bank grew from $150 million in 2007 to $205 million in 2012. s' Green Gian t Daycare Center purchased new furniture for its toddler room. The estimated useful life of the furniture is 10 years The total (a) Assume that deposits grew at a rate that is cost was $3650 and tho value at the end of 10 years is expected to be S (a) What is the rate of change for this function? linear. Calculate the rate of change (b) Let x0 correspond to the year 2007. Write a linear function that can be used to predict future deposits of the years after 2007 (c) Calculate f(10) and explain its meaning. (b) Write a function that can be used to estimate during the 10-year period. 15. A businessman decides to purchase a second facility after his annual sales reach S1,500,000. In 2006, annual sales were s800,000, and in 2011, they were $1,000,000 Calculate 8) and explain its meaning. (c) Use the data in the tables to write a linear function 9. See Table 4-10 (a) Assume that the growth is linear and calculate the rate of change. (b) Let x 0 correspond to the year 2006. Write TABLE 4-10 linear function that can be used to predict 20 25 future annual sales after 2006. (C Use this function equation to determine the year that his annual sales will reach S1,500,000. 10. ee Table 4-11 TABLE 4-11 16.)Tbe cost of manufacturing goods is a linear function that includes fixed costs, such as utilities and rent, and per unit costs of manufacturing each individual item. In a month, Marvin Stephen Manufatturins Company produces 100 units for $8400 and 250 units for $9000 (a) Assume that the cost of production is a 6 11. See Table 4-12 linear function and find the rate of change. If the fixed costs of production are $8000 per month, write a linear function to model the monthly production of x units How many units can be produced for a cost of $10,000? TABLE 4-12 (b) 10 5 (e) 12. See Table 4-13 17. The average yearly in-state tuition and fees charged by U.S. public universities for the years 2008-2010 are shown in Table 4-14. TABLE 4-13 10 10 20 30 15 TABLE 4-14 13. The population of a small town grew from 450 in 2008 2009 2001 to 650 in 2011 Average Tuition 3536 S4115 $4694 (a) Assume that the growth is linear and calculate the rate of change What is the rate of change or slope of this function? Write the linear function model for these data. Let $3536 be the initial value of the function with 2008 as year 0. (a) (b) Let x=0 correspond to the year 2001. Write a linear function that can be used to predict future population after 2001 (b) (c) Calculate f(15) and explain its meaning.

Explanation / Answer

Question 8

(a) Here rate of change = (Intitial value - Value at t years)/ number of years = ($ 3650 - $ 250)/ 10 = $ 340

(b) Here the function is a linear function

f(V) = 3650 - 340t where t is the time in years

(c) Here for t = 8 years

V = 3650 - 340 * 8 = $ 930

so, It means that after 8 years the value of the furniture would be $ 930

Question 10

Here first we have to find slope here

m = (yfinal - yinitial)/ (xfinal - xinitial) = (7/2 - (-5/2) / (6 - (-2)) = 6/8 = 0.75

so, linear equation

y -yinitial = m * (x- xinitial)

y - 5/2 = 0.75 * (x + 5/2)

y = 0.75x - 1

Question 12

Here first we have to find slope here

m = (yfinal - yinitial)/ (xfinal - xinitial) = (-20 - (-5) / (30 - 0) =-0.5

so, linear equation

y -yinitial = m * (x- xinitial)

y + 5 = -0.5 * (x -0)

y = -0.5x -5

Question 12

Rate of change = (Final cost - Intitial cost)/ diference in products = ($ 9000 - $ 8400)/ (250 - 100) = 4

(b) Fixed cost = $ 8000

so, f(C) = 8000 + 4x

(c) Cost = $ 10000

10000 = 8000 + 4x

4x = 2000

x = 500

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