Exponential Functions and Logarithms I Flashcards
What is an exponential function?
In an exponential function, what does the constant b and the variable x represent?
b is the base and x is the exponent!
What is the difference between exponential growth and decay?
b>1 in exponential growth, b<1 in exponential decay
What would happen is b = 1 in an exponential function?
It wouldn’t be an exponential function anymore, just a line.
What are four elements that exponential functions always have?
What are two other forms of exponential functions then f(x) =b^x?
Since logarithmic functions are the inverse of exponential functions, what would be the four elements that they always have?
Complete the 4 exponential laws:
Prove that this function is an exponential function in disguise.
Write an formula representing the growth of the population of bacteria after t hours. f(x) = A*B^x
What is Eulier’s number?
e = 2.71828. A very important mathematical constant and is the base for natural logarithms. An irrational number represented by the letter e, Euler’s number is 2.71828…, where the digits go on forever in a series that never ends or repeats (similar to pi)
What is special about Eulier’s number?
What is compounding interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest
What is the formula of the compounding model? Describe the variables as well. (4)
What would be the compound interest formula if we would compound once a year?
What would be the compound interest formula if we would compound 6 times a year?
What would be the compound interest formula if we would compound 12 times in a two-year period?
What would be the compound interest formula if we would compound every day for 5 years?
What would be the compound interest formula if we would continuously without stopping?
What is a logarithm?
It is the opposite of an exponential function
What does Loga b =c represent?
c is the exponent that must be put on a to give b.
Convert the logarithmic form to the exponential form. Use b, y and x.
What are the two special bases that come up most of the time in logarithms?
log base 10 and log base e
Which of the two special logarithm bases is called the common logarithm?
log base 10
Which of the two special logarithm bases is called the common logarithm?
log base e written as ln x
Draw y = b^x knowing that b>0 and is not equal to 1 on a graph:
Draw a common logarithmic function.
any logarithmic function that has base 10.
Draw a natural logarithmic function
log base e
Draw ln (x) on a graph:
Since exponential and logarithmic functions are inverse of each other, what does this statement show?
Log base b of b^x = x
When you plug in exponential into a logarithmic function, they cancel out and it will always give you back the exponent.
Solve:
You’re just left with 20
Solve
50
Can you log a negative number?
Nope!
Solve:
12
Solve:
pi
What are the three logarithmic properties and which one is the most important?
- logb(A) + logb (C) = logb (C*A)
- A*logb (C) = logb (C^A)
- logb(A) = logc(A)/ logc (B)
The most Important is the third.
What is the relationship between exponential and logarithmic functions?
Logarithms are the inverse of exponential functions
What are 4 facts about logarithms on a graph?
Because the inside needs to be positive. We can’t log or ln negative numbers.
What is the dom and range of f(x) and f(x) inverse if:
Use transformations to sketch:
Basic function of y=2^x
Shifted to the right by 1
Shifted down by 3
New asymptote is at y = -3
Use transformations to sketch.
Shifted to the right by 2 and reflected over the y-axis
