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Warm Up Section 3.7B (1). Simplify: (3 x -2 y 4 )(4 x -3 y - 4 )

Warm Up Section 3.7B (1). Simplify: (3 x -2 y 4 )(4 x -3 y - 4 ) (2). If f ( x ) = 3 x + 7 and g ( x ) = x 2 – 4, find a. ( f + g )( x ) b. ( f – g )( x ) c. f ( g ( x )) (3). If h ( x ) = 7 x + 2, find h -1 ( x ).

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Warm Up Section 3.7B (1). Simplify: (3 x -2 y 4 )(4 x -3 y - 4 )

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  1. Warm Up Section 3.7B (1). Simplify: (3x-2y4)(4x-3y-4) (2). If f(x) = 3x + 7 and g(x) = x2 – 4, find a. (f + g)(x) b. (f – g)(x) c. f(g(x)) (3). If h(x) = 7x + 2, find h-1(x). (4). Write an expression for the 17th term of a geometric sequence in which a1 = 4 and r = -5 (5). Identify the domain and range of y = 6x – 3

  2. Answers to Warm Up Section 3.7B (1). (3x-2y4)(4x-3y-4) = 12x-5y0 = (2a). (f + g)(x) = x2 + 3x + 3 (2b). (f – g)(x) = -x2 +3x + 11 (2c). f(g(x)) = 3x2 – 5 (3). h-1(x) = (x – 2)/7 (4). a17 = 4(-5)16 (5). y = 6x – 3 Domain: all reals Range: y > -3 12 x5

  3. 3.6B HW ans 1. Arithmetic d=2 2. Geometric r=2 3. Geometric r = 1/2 4. None Geometric r=3 6. Geometric r = 1/3 7. 8. 9. a12 = 354294 a12 = 0.0000000004 a12 = -1/64

  4. 10. 12. 11. 13. 14. 93 15. 134.97 or 16. 63.9375 or 17. 236192

  5. Application of Exponential Functions Section 3.7B Standard: MM2A2 Essential Question: How do I apply exponential functions to real world situations?

  6. 1. The formula C = 2πrgives the circumference of a circle of radius, r. Write the inverse function, and use it to find the radius of a circle whose circumference is 14 inches. C = 2r Inverse: divide by 2 Let C = 14: so The radius is approximately 2.23 inches.

  7. 2. An infectious virus is defined by its infectivity, or how contagious the virus is to humans. The number of people (in thousands) expected to contract the virus within 6 months is modeled by y = 1.04(8.35)xwhere x is the infectivity rating of the virus. If the infectivity rating is 2.5, how many people would you expect to be infected within 6 months? y = 1.04(8.35)2.5 y ≈ 209.532 (thousand) In 6 months 209,532 people will be infected.

  8. 3. Compound interest is interest paid on the initial investment, called the principal and on previously earned interest. Consider an initial investment (principal) deposited in an account that pays interest at an annual rate, (expressed as a decimal), compounded times per year. The amount in the account after years is given by the equationYou deposit $3500 in an account that earns 2.5% annual interest. Find the balance after one year if the interest is compounded with the given frequency: a. annually b. quarterly c. monthly

  9. (3a). (3b). (3c).

  10. 4. A Petri dish contains 3 amoebas. An amoeba is a microorganism that reproduces using the process of fission, by simply dividing itself into two smaller amoebas. Once the new amoebas mature, they will go through the same process. a. Write the terms of the sequence describing the first four generations of the amoeba in the Petri dish.

  11. 4. A Petri dish contains 3 amoebas. An amoeba is a microorganism that reproduces using the process of fission, by simply dividing itself into two smaller amoebas. Once the new amoebas mature, they will go through the same process. b. Write a rule for the nth term of the sequence.c. Find the 10th term of the sequence and describe in words what this term represents. an = 3(2)n -1 a10 = 3(2)9a10 = 1536 The 10th generation will have are 1,536 amoebas if none die!

  12. 5. You invest $5000 in a retirement plan. The plan is expected to have an annual rate of return of 8%. Write an exponential model for the amount of money in the plan after years. What is the balance of the account after 25 years? How much would you have after 25 years if the initial investment had been $10,000? y = 5000(1 + 0.08)t y = 5000(1.08)25 = 34,242.38 y = 10000(1.08)25= 68,484.75

  13. 6. You have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.a. Use function notation to describe your cost, f(x), using only the coupon.b. Use function notation to describe your cost, g(x), using only the discount. f(x) = x – 200 g(x) = 0.8x

  14. 6. You have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.c. Form the composition of the functions f and g that represents your cost if you apply the coupon first, then apply the 20% discount. g(f(x)) = g(x – 200) = 0.8(x – 200) = 0.8x – 160

  15. 6. You have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.d. Form the composition of the functions f and g that represents your cost if you apply the discount first, then apply the coupon. f(g(x)) = f(0.8x) = 0.8x – 200 e. You would pay less for the computer if you appliedthe discount first.

  16. 7. You drop a ball from a height of 66 inches and the ball starts bouncing. After each bounce, the ball reaches a height that is 80% of the previous height. Write a rule for the height of the ball after the nth bounce. Then find the height of the ball after the sixth bounce. y = a(1 – r)n y = 66(0.8)6 y ≈ 17.3 The height of the ball after the sixth bounce is approximately 17.3 inches.

  17. 8. The euro is the unit of currency for the European Union. On a certain day, the number of euros, E, which could be obtained for D dollars, was given by this function: E = 0.81419D. Find the inverse of this function, then use the inverse to find the number of dollars that could be obtained for 250 euros on that day. Inverse: Let E = 250 250 Euros is approximately $307.05

  18. 9. From 2002 to 2007, the number n (in millions) of blank DVDs a company sold can be modeled by n = 0.42(2.47)t where t is the number of years since 2002. Identify the initial amount, the growth factor, and the annual percent increase. How many DVD’s were sold in 2006? • The initial amount is 0.42 million DVDs • The growth factor is 2.47 • The annual percent increase is 147% • y = 0.42(1 + 1.47)t • n = 0.42(2.47)4 • 15.63 million DVDs were sold in 2006

  19. 10. Your sister tells you a secret. You see no harm in telling two friends. After this second passing of the secret, 4 people now know the secret. If each of these people tell 2 new people, after the 3rd passing 8 people will know. If this pattern continues, how many people will know the secret after 10 passings? 210 = 1024 1024 people will know after 10 passings.

  20. 11. The number of wolves in the wild in the northern section of Cataragas County is decreasing at the rate of 3.5% per year. Your environmental studies class has counted 80 wolves in the area. If this rate continues, how many wolves will remain after 50 years? y = a(1 – r)n y = 80(1 – 0.035)50 y = 13.47 Approximately 13 wolves remain after 50 years.

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