1. Problem Solving Exponential & Scientific Notation

2. Karan brought 6 mice. Every month the number of mice she has doubles
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%
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( )t or…
y = 2,500•(1.03)t

6. The amount of rural acreage in a county is declining by 6. 5% per year
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( )t or…
y = 525,000(0.935)t

7. 6) Earth is approximately 1. 5 x 108 km from the sun
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 102 or 500 seconds

8. 7) Light travels approximately 6 x 1012 miles per year
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
M = 18 x 1014
= 1,800,000,000,000,000 miles
or M = 1.8 x 1015 miles

9. Scientific Notation = 2.5 x 107
The side of a square is 5 x 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. Area = l • w Area = n10 • n4 a) n10 + 4 «««« b) n10•4 c) n10 + n4
9) Given the following rectangle. Which of the following would be used to find the area of the shape?
n10
a) n10 + 4
b) n10•4
c) n10 + n4
d) 2n10•4
«««« n4
Area = l • w
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( )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? y = 3(5)x y = ½(1.5)x y = 6(⅓)x y = 3x
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( )x
y = ⅛x y = 6x
Linear
Linear