Problem SolvingExponential &

Scientific Notation

1) 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 Modely = (initial)•(constant multiplier)x

M = (6 mice)•(doubling)x

Function M = 6•2x

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 Modely = (initial)•(constant multiplier)x

B = (400)•(tripling)t

Function B = 400•3t

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 Modely = (initial)•(constant multiplier)x

A = (144)•(cut in half)t

Function A = 144•(½)t

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)t or…

y = 2,500•(1.03)t

5) 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)t or…

y = 525,000(0.935)t

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

1.5 x 108 = (3 x 105) • t

t = 5 x 102 or 500 seconds

Miles = (miles per second) • (time) solve for ‘t’ by dividing

1.5 x 108 = t3 x 105

0.5 x 103 = t … which has to be fixed

7) Light travels approximately 6 x 1012 miles per year. How far away would the light be in 300 years? Distance = rate • time

M = (6 x 1012)• (3 x 102)

or M = 1.8 x 1015 miles

Miles = (miles per year) • (years)

solve by multiplying

M = 18 x 1014 = 1,800,000,000,000,000 miles

8) The side of a square is 5 x 103. Write the area of the square in scientific notation and standard notation.Area = s2

A = 25 x 106

A = (5 x 103)2 solve by raising to a power

Scientific Notation = 2.5 x 107

Standard Notation = 25,000,000

9) Given the following rectangle. Which of the following would be used to find the area of the shape? n10

n4a) n10 + 4

b) n10•4

c) n10 + n4

d) 2n10•4Area = l • wArea = n10 • n4

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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 = (2x2)3 V = 8x6

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

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