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What are the basic techniques for solving exponential equations?
The basic techniques for solving exponential equations are taking logarithms, using properties of exponents, and simplifying the equation to isolate the variable.
Is the following sequence Arithmetic, Geometric or Neither? 12, 14, 16, 18, 20,.....
Arithmetic
The value of a smartphone depreciates at a rate of 15% per year. If the initial value is $1,000, find the smartphone's value after 3 years. Answer to the Hundredth
614.125
Find the common difference or ratio to find the next term of the sequence:
-1, -2, -4, -8, __
r= 2
n5= -16
Find the Domain and Range of f(x)=5^(x)
Domain: (−∞,∞)
Range: (0,∞)
What Equation is this?
Y=abx
Exponential Function
How can logarithmic functions and equations be used to solve exponential equations?
Logarithmic functions and equations can be used to solve exponential equations by converting the equation into a logarithmic form and then using the properties of logarithms to simplify and solve for the variable.
Is the following sequence Arithmetic, Geometric or Neither? 4, 11, 17, 24, 34,....
What is neither.
The value of a computer depreciates at a rate of 8% per year. If the initial value is $2,500, find the computer's value after 7 years. Answer to the Hundredth
1394.62
Find the common difference or ratio to find the next 2 terms in the sequence
0, -4, -8, -12,__, __,...
r= -4
n5= -16
n6= -20
Find the Domain and Range of f(x)=6^(x) -5
Domain: (−∞,∞)
Range: (−5,∞)
What Equation is this?
y=a(1-r)t
Exponential Decay
Solve the exponential equation: 3^(2x) = 27.
x=3/2
Is the following sequence Arithmetic, Geometric or Neither? 3, 8, 13, 18, 23,.....
What is an Arithmetic Sequence.
The population of rabbits doubles every 6 months. If there are initially 100 rabbits, how many will there be after 2 years? Applications of Exponential Growth and Decay
1600
Find the common difference or ratio to find the next 4 terms of the sequence. Remember how I want the answer.
-1, -0.5, -0.25, -0.125, __, __, __, __,...
r= 1/2
n5= -1/16
n6= -1/32
n7= -1/64
n8= -1/128
Find the Domain and Range of f(x)=-2^(x) +1
Domain: (−∞,∞)
Range: (−∞,1)
What is the Formulas for Recursive for both Geometric and Arithmetic?
Arithmetic: an=an-1+d
Geometric: an=r*an-1
Solve the exponential equation: 2^(x + 1) = 8.
x=2
Is the following sequence Arithmetic, Geometric or Neither? If so, what is the common difference or common ratio? 500, 460, 420, 380, 340,.....
What is an Arithmetic Sequence with a common difference of -40?
The population of a city is currently 500,000, and it is growing exponentially at a rate of 3% per year. Estimate the population after 20 years. Answer to the Hundredth
903,055.62
Find the first and fifth terms
__, 10, -50, 250, __,...
r= -5
n1= -2
n5= -1,250
Find the Domain and Range of f(x)=-3^(x) -5
Domain: (−∞,∞)
Range: (−∞,-5)
What Equation is this?
Y= a(1+r)t
Exponential Growth
Give an example of an application problem that involves solving exponential equations.
Determining the time it takes for a radioactive substance to decay to a certain level given its half-life.
Is the following sequence Arithmetic, Geometric or Neither? If so, what is the common difference or common ratio? 3, 15, 75, 375,........
What is a Geometric Sequence with the common ratio of 5?
Medication has a half-life of 6 hours. If a patient is given a 200 mg dose, how much will remain in their system after 24 hours? Answer to the Tenth
12.5
Find the first and fourth terms
__, 20, 29, __, 47,...
d= 9
n1= 11
n4= 38
Find the Domain and Range f(x)=-3^(x)+5
Domain: (−∞,∞)
Range: (−∞,5)
What Equation is this? What does each letter mean?
A=P(1+r/n)nt
Compound Interest
A=Current Amount
P= Principal
r=rate
n=number of times per year
t=time