6.1 Key Features of Exponential Functions
6.2 Exponential Models
6.3 Logarithms
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Exponential and Logarithmic Equations
100
What is the domain, range, asymptotes, and intercepts for (parent) exponential functions
Domain: All reals, Range: y>0, y-int at (0,1), HA at y=0
100
What is the difference between interest, compounding interest, and continuously compounding interest?
Interest: price paid for borrowing money for a period of time, paid at the end of lending period
Compounding interest: Interest that is charged periodically, every time an interval passes and increases the amount of principal owed
Continuously compounding: interest is charged continuously and constantly added to the principal
100
What is the domain, range, asymptotes, and intercepts for (parent) logarithmic functions
Domain: x>0, Range: all reals, x-int at (1,0), VA at x=0
100
A farmer monitoring an insect plague notices that the area affected by the insects is given by A_n=1000\times2^(0.7n) square meters, where n is the number of weeks after the initial observation. Estimate the time taken for the affected area to reach 5000 square meters.
It will take about 3 weeks and 2 days (or when n is about 3.32 weeks)
100
Condense into a single logarithm
9lnx-3lny
ln (x^9/y^3)
100
5^(3a)=5^(2a+2)
a=2
200
Evaluate the function at x=2 , f(x)=1/3\*6^x
f(2)=12
200
When you were born, your grandparents deposited $5,000 into a college savings account paying 6% continuously compounded interest. What is the balance after 15 years?
$12,298.01
200
Simplify 12^(log_12(144)
144
200
Given the below graphs, determine which graph is y=lnx and which is y=ln(x-2) and explain why.
Graph A is y=lnx as the x-intercept is at (1,0)
200
Without a calculator:
Expand log(6/11)^5
5log6-5log11
200
log_4(x^2+11)=log_4(-10x+2)
x=-9, x=-1
300
Evaluate the function at x=-2, f(x)=10\*2^x
f(-2)=5/2
300
When you were born, your grandparents deposited $5,000 into a college savings account paying 6% continuously compounded interest. How long will it take the balance to reach at least $17,000?
At least 20.396 years
300
Rewrite log_u(15/16)=x in exponential form
u^x=15/16
300
You have $5000 to invest in an account that pays 5.2% compounded annual interest. How long will it take for your investment to reach $20,000?
It will take at least 28 years (t=27.3)
300
Expand
log_8(a/b^5)^5
5log_8a-25log_8b
300
log_6(x-10)+10=13
x=226
400
Identify the transformations and graph the parent function and the transformation of:
y=3(1/3)^x
Parent function: y=(1/3)^x
Vertical stretch of 3
400
A philanthropist pledges to donate 12% of a fund each year. If the fund initially has $654,000.00, how much will the fund have after 8 years?
$235,200.98
400
without a calculator
Evaluate log_64(4)
1/3
400
Expand the logarithm
log_8(x/y^6)^4
4log_8x-24log_8y
400
64^(3x)=16
x=2/9
500
Sketch the graph of the function: y=4\*(1/2)^(x+1)-1
500
Rentals in a high rise apartment building get more expensive higher up as the views get better. The ground floor (floor 0) the rent is $1,900.00 and the rent increases 3% per floor. What is the rent on the 10th floor?
$2,553.44
500
Identify the transformations and graph the parent function and the transformation of:
y=1/2\*log_(1/2)x-2
Vertical compression of 1/2, down by 2
500
The number n of college graduates in thousands after t years can be modeled by n=46log_5(t+3) . Let t=0 represent the year 1985. How many college graduates were there in 2003?
87,017 graduates
500
Condense into a single logarithm
log_6(11)+log_6(12)/3+log_6(5)/3
log_6(11\root(3)60)
500
log_2(2x^2-12x)=log_2(-32+x^2)
x=8
600
Write an equation for the graph below:
y=-2\*2^(x+1)-1
600
The radioactive isotope Radium-226 decays exponentially. If the mass was 35625.99 grams 9 thousand years ago and the current mass is 743.10 grams, what will the mass be 7 thousand years from now?
36.63 grams
600
Find the inverse function of y=log_2(x+5)-9
y=2^(x+9)-5
600
In 2003, the population of the state of New York was 10.78 million people. in 1990, it was 7.99 million. Using y=ae^(kt) , determine the value of k, New York's relative rate of growth.
k=0.023
600
Simplify 2(log2x-logy)-(log3+2log5)
log((4x^2)/(75y^2))
600
log_4(8)+log_4(2x^2)=3
x=2 , x=-2
700
The below table shows the average salary of baseball players since 1984. What is the estimated salary of a baseball player in the year 2005 to the nearest thousand dollars?
In 2005, it is estimated that a player will earn $14,387,218
700
Atmospheric pressure decreases exponentially as elevation increases. If the pressure is 31.6 inHg in a valley 0.1 miles below sea level and the pressure at sea level is 31.0 inHg, what is the pressure at 8.0 miles above sea level?
6.69 inHg at 8 miles above sea level
700
In 2003, the population of the state of New York was 10.78 million people. in 1990, it was 7.99 million.
Nevada's population in 1990 was 14.2 million and can be modeled by y=14.2e^(0.0079t) . Determine when New York's population will surpass Nevada's.
NY will surpass Nevada in 2028 or when t=38.079 years
700
log_15(x^2-12x)=log_15(-25-2x)
No Solution!