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MATH201 Elementary Functions > Exponential Functions and Logarithms I > Flashcards

Exponential Functions and Logarithms I Flashcards

1
Q

What is an exponential function?

A
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2
Q

In an exponential function, what does the constant b and the variable x represent?

A

b is the base and x is the exponent!

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3
Q

What is the difference between exponential growth and decay?

A

b>1 in exponential growth, b<1 in exponential decay

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4
Q

What would happen is b = 1 in an exponential function?

A

It wouldn’t be an exponential function anymore, just a line.

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5
Q

What are four elements that exponential functions always have?

A
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6
Q

What are two other forms of exponential functions then f(x) =b^x?

A
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7
Q

Since logarithmic functions are the inverse of exponential functions, what would be the four elements that they always have?

A
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8
Q

Complete the 4 exponential laws:

A
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9
Q

Prove that this function is an exponential function in disguise.

A
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10
Q

Write an formula representing the growth of the population of bacteria after t hours. f(x) = A*B^x

A
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11
Q

What is Eulier’s number?

A

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)

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12
Q

What is special about Eulier’s number?

A
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13
Q

What is compounding interest?

A

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

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14
Q

What is the formula of the compounding model? Describe the variables as well. (4)

A
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15
Q

What would be the compound interest formula if we would compound once a year?

A
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16
Q

What would be the compound interest formula if we would compound 6 times a year?

A
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17
Q

What would be the compound interest formula if we would compound 12 times in a two-year period?

A
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18
Q

What would be the compound interest formula if we would compound every day for 5 years?

A
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19
Q

What would be the compound interest formula if we would continuously without stopping?

A
20
Q
A
21
Q

What is a logarithm?

A

It is the opposite of an exponential function

22
Q

What does Loga b =c represent?

A

c is the exponent that must be put on a to give b.

23
Q

Convert the logarithmic form to the exponential form. Use b, y and x.

A
24
Q

What are the two special bases that come up most of the time in logarithms?

A

log base 10 and log base e

25
Q

Which of the two special logarithm bases is called the common logarithm?

A

log base 10

26
Q

Which of the two special logarithm bases is called the common logarithm?

A

log base e written as ln x

27
Q

Draw y = b^x knowing that b>0 and is not equal to 1 on a graph:

A
28
Q

Draw a common logarithmic function.

A

any logarithmic function that has base 10.

29
Q

Draw a natural logarithmic function

A

log base e

30
Q

Draw ln (x) on a graph:

A
31
Q
A
32
Q
A
33
Q

Since exponential and logarithmic functions are inverse of each other, what does this statement show?

A

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.

34
Q

Solve:

A

You’re just left with 20

35
Q

Solve

A

50

36
Q

Can you log a negative number?

A

Nope!

37
Q

Solve:

A

12

38
Q

Solve:

A

pi

39
Q

What are the three logarithmic properties and which one is the most important?

A
  1. logb(A) + logb (C) = logb (C*A)
  2. A*logb (C) = logb (C^A)
  3. logb(A) = logc(A)/ logc (B)
    The most Important is the third.
40
Q

What is the relationship between exponential and logarithmic functions?

A

Logarithms are the inverse of exponential functions

41
Q

What are 4 facts about logarithms on a graph?

A
42
Q
A
43
Q
A

Because the inside needs to be positive. We can’t log or ln negative numbers.

44
Q

What is the dom and range of f(x) and f(x) inverse if:

A
45
Q

Use transformations to sketch:

A

Basic function of y=2^x
Shifted to the right by 1
Shifted down by 3
New asymptote is at y = -3

46
Q

Use transformations to sketch.

A

Shifted to the right by 2 and reflected over the y-axis

MATH201 Elementary Functions (11 decks)

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