Problem Solving Exponential & Scientific Notation

1. Problem SolvingExponential & Scientific Notation

2. Karan brought 6 mice. Every month the number of mice she has doubles. After x months she has M mice total. Write a function to represent this situation. Exponential Growth Model y = (initial)•(constant multiplier)x M = (6 mice)•(doubling)x Function M = 6•2x

3. 2) If there are initially 400 bacteria in a culture, and the number of bacteria triple each hour, write an equation to model how many total bacteria, B, will be there in “t” hours. Exponential Growth Model y = (initial)•(constant multiplier)x B = (400)•(tripling)t Function B = 400•3t

4. 3) The amount, A, of a 144 grams of a certain radioactive material remaining after “t” years changes by being cut if half each year. Write a function to model this change. Exponential Decay Model y = (initial)•(constant multiplier)x A = (144)•(cut in half)t Function A = 144•(½)t

5. 4) $2,500 was invested in a bank with a compounded annual rate of 3%. Write a function to determine how much money will be in the bank after “t” years. Exp Growth Model w % y = a(1 + r)t y = 2,500(1 + 0.03)tor… y = 2,500•(1.03)t

6. The amount of rural acreage in a county is declining by 6.5% per year. If the county had 525,000 acres originally, write a function that would represent the amount of acres as time passes. Exp Decay Model with %y = a(1 - r)t y = 525,000(1 - 0.065)tor… y = 525,000(0.935)t

7. 6) Earth is approximately 1.5 x 108 km from the sun. Light travels at approximately 3 x 105 km per second. How long does it take light to travel from the sun to the earth? Distance = rate • time Miles = (miles per second) • (time) 1.5 x 108= (3 x 105) • t solve for ‘t’ by dividing 1.5 x 108= t 3 x 105 0.5 x 103 = t … which has to be fixed t = 5 x 102or 500 seconds

8. 7) Light travels approximately 6 x 1012 miles per year. How far away would the light be in 300 years? Distance = rate • time Miles= (miles per year) • (years) M =(6 x 1012)• (3 x 102) solve by multiplying =1,800,000,000,000,000 miles M =18 x 1014 orM = 1.8 x 1015miles

9. The side of a square is 5 x 103. Write the area of the square in scientific notation and standard notation. Area = s2 A = (5 x 103)2 solve by raising to a power A = 25 x 106 Standard Notation = 25,000,000 Scientific Notation = 2.5 x 107

10. 9) Given the following rectangle. Which of the following would be used to find the area of the shape? n10 a) n10 + 4 «««« n4 b) n10•4 c) n10 + n4 Area = l • w d) 2n10•4 Area = n10 • n4

11. YOUR TURN TO TRY SOME --Write a function that can be used to answer the following: 10) The measurement of the edge of a cube is represented by 2x2. What is a simplified equation that would represent the volume of the cube? 11) A culture of bacteria doubles every day. If the culture has 6 grams of bacteria today, write an equation that will determine the total number of bacteria in x days.  12) For my birthday I received $150. I plan to put it in the bank that gives 1.2% interest compounded annually. How much money will I have after 10 years?  13) A company's annual revenue in 2001 was $120,000. After 2001, business was reduced at a rate of 4% per year. What would be the annual revenue of that business this year in 2012? V = 8x6 V = (2x2)3 B = 6•(2)x T = 150(1+0.012)10 or T = 150(1.012)10 R = 120,000(1-0.04)11 or R = 120,000(0.96)11

12. GROWTH OR DECAY? Circle the functions that show Exponential Growth. Underline the functions that show Exponential Decay. y = 3(5)x y = ½(1.5)x y = 6(⅓)x y = 3x y = 100(¾)x y = 4,000(1 + 0.05)x y = ⅛x + 5 y = 6x Linear Linear