3.1 - Exponential Functions
If you have 2000 compounded monthly at a 5% annual rate, how much money will you have after 10 years?
$3,294.02
Rewrite this equation in logarithmic form:
35 = 243
log3243 = 5
NO CALCULATOR
Expand:
log47x
log47 + log4x
SOLVE
log9(4 + x) = log9(2x - 1)
x = 5
Find the intensity of an earthquake that is measured on the Richter Scale as a R = 5.5.
R = log10I/Io
316,227.766
Plutonium has a half-life of 14 years and is modeled by the equation:
Q = 50(.5)t/14
How much plutonium is left after 50 years?
4.21 grams.
NO CALCULATOR
Simplify:
log216
4
NO CALCULATOR
Condense
3lnx + 2lny - 4lnz
(x3y2)/z4
SOLVE
65x = 3000
x = .8937
The average number N of words per minute that the students in a first grade class could read after t weeks of school is modeled by:
N = 62/(1 + 5.4e-0.24t)
How many words did they students learn in 2 weeks?
About 14 words.
You had invested $20,000 compounded continuously at an annual rate of 8% for 12 years while you were saving up for a house. If your new house requires a down payment of $50,000, how much would you have left over?
$2,233.93
NO CALCULATOR
Simplify:
log4(1/8)
-3/2
NO CALCULATOR
5 ln e4
20
SOLVE
log (x - 3) = 2
x = 103
The average number N of words per minute that the students in a first grade class could read after t weeks of school is modeled by:
N = 62/(1 + 5.4e-0.24t)
How long did it take the students to learn 40 words?
About 9.5 weeks.
NO CALCULATOR
Graph the following equation (show three points in a table) and draw your asymptote on your graph.
y = 2x + 4
(0,5)
(1,6)
(2,8)
NO CALCULATOR
Graph the following equation (show three points in a table) and draw your asymptote on your graph.
y = 1 + log2x
(1,1)
(2,2)
(4,3)
NO CALCULATOR
Evaluate
log42 + log416
5/2
SOLVE
6(8-2-x) + 15 = 2601
x = -4.9172
The population P (in thousands) in Pittsburgh from 2000 to 2008 (with t=0 corresponding to 2000) can be modeled by the equation:
P = 333.68e-0.0099t, where t is the year.
According to the model, what year will the population reach 290,000?
2014
NO CALCULATOR
Graph the following equation (show three points in a table) and draw your asymptote on your graph.
y = 2x+3 -2
(-3,-1)
(-2,0)
(-1,2)
(0,6)
NO CALCULATOR
Graph the following equation (show three points in a table) and draw your asymptote on your graph.
y = -3 + log2(x-1)
(2,3)
(3,4)
(5,5)
NO CALCULATOR
Evaluate:
log92 - log954
-3/2
SOLVE
2e2x + ex - 3 = 0
x = 0
Find an EXPONENTIAL model for the data below AND find out how much revenue was collected in 2015. (Use t = 1 for 2001)
Year - 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008
Revenue - 148.8, 177.8, 209.9, 230.3, 309.4, 433.2, 499.7, 581.9
y = 115.4671(1.2270)x
$2483.86