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# Module 23

### Exponential Functions

Solve for X 4^X=1024 X=5
Solve for X 5^X=625 X=4
Solve for X 4^X=32 X=5/2
Solve for X 16^X=32 X=32
Solve for X 10000^X=100000 X=10
Solve for X 64^5X=16^X+3 X=6/13
An item weighs 4040 lbs and has a decay rate of 1.41.4​% per day. How much will still remain after 5050 days? Use: Y=40(0.986)^X let x be 5050. 19.77 lbs would remain
The equation y=118.74118.74(1.129)^ X gives the number of cell phone users (in millions) in 1 country for the years of 2002-2009. X=0 corresponds to​ 2002, x=1 corresponds to​ 2003, and so on. Predict the number of cell phone users in 2011 353.9 million cell phone users in 2011
If b>0 and b doesn't equal 1 than B^X=B^Y is equivalent to X=Y
Exponential Function is A function of the form f(x)=b^X if b>0 if b is not 1 and X is a real number
Why don't we want the base b to be 1? It would be a constant function. Any number times 1 will equal 1
Why don't we want the base b to be a negative number? We want real numbers, not complex numbers,
27^x+1=9 x= -1/3
Exponential Function Graph f(x)=b^x, b>0, b doesn't equal 1 -one to one function -y intercept (0,1) -no x intercept
Exponential Function domain is (- infinity, infinity)
Exponential Function range is (0, infinity)
The graph is a decreasing graph if b is between 0 and 1
The graph is an increasing graph if b>1
Steps to solve 16^x=8 Make bases the same (2^4)^x=2^3 Simplify 2^4x=2^3 Set exponents equal 4x/4=3/4 x=3/4
A quantity that grows or decays by the same percent at regular time intervals is said to Grow exponentially or decay exponentially
Exponential Decay formula Y=C(1-r)^x C=original amount R=growth rate (often a percent, turn into a decimal before adding into equation) X=number of time intervals (1-r)= growth factor
Exponential Growth formula Y=C(1+r)^x C=original amount R=growth rate ( often a percent, turn into decimal before adding into equation) X= number of time intervals (1+r)= growth factor
Half life is the amount of time it takes for half of something to decay or disappear
How to find X for half life in equation y=C(1-r)^X? number of years/half life= X
In the formula for half life y=C(1-r)^X what is r? r is the growth rate, in the formula for half life r is 50% which is written into decimal form 0.50
Original amount=305, Growth rate=5%, # of years=8 What is the amount in 8 years? (round to the nearest whole #) y=305(1+0.05)^8 The amount in 8 years is around 451
Current employees= 640, percent decreasing per year=5%, How many employees will there be in 10 years? (round to the nearest whole 3) y=640(1-0.05)^10 There will be around 383 employees left in 10 years
Original amount=21 grams, half life=152, #of years=500, What is x? How many grams will there be left (round to nearest whole number? 500 (years) /152 (half life)=3.3 (time interval) x=3.3 Y=21(1-0.50)^3.3= around 2.1 grams will be left
The equation y=109.54(1.107)^x gives the number of cellular phone users y​ (in millions) in a country for the years 2002 through 2009. If x=0 corresponds to​ 2002, x=1 corresponds to​ 2003, What is the number of cell phone users in the year 2014 In the year 2014 the number of cell phone users in the country will be about 371 million
Find the amount Sam owes at the end of 6 years if ​\$5600 is loaned to her at a rate of 7 % compounded monthly. Use A=P(1+r/n)^nt The amount owed is 8512.59
Created by: SamLarzelere