Exponential Functions and Logarithms I

Question 1

What is an exponential function?

Answer 1

Question 2

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

Answer 2

b is the base and x is the exponent!

Question 3

What is the difference between exponential growth and decay?

Answer 3

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

Question 4

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

Answer 4

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

Question 5

What are four elements that exponential functions always have?

Answer 5

Question 6

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

Answer 6

Question 7

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

Answer 7

Question 8

Complete the 4 exponential laws:

Answer 8

Question 9

Prove that this function is an exponential function in disguise.

Answer 9

Question 10

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

Answer 10

Question 11

What is Eulier’s number?

Answer 11

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)

Question 12

What is special about Eulier’s number?

Answer 12

Question 13

What is compounding interest?

Answer 13

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

Question 14

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

Answer 14

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Answer 19

Question 20

Answer 20

Question 21

What is a logarithm?

Answer 21

It is the opposite of an exponential function

Question 22

What does Loga b =c represent?

Answer 22

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

Question 23

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

Answer 23

Question 24

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

Answer 24

log base 10 and log base e

Question 25

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

Answer 25

log base 10

Question 26

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

Answer 26

log base e written as ln x

Question 27

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

Answer 27

Question 28

Draw a common logarithmic function.

Answer 28

any logarithmic function that has base 10.

Question 29

Draw a natural logarithmic function

Answer 29

log base e

Question 30

Draw ln (x) on a graph:

Answer 30

Question 31

Answer 31

Question 32

Answer 32

Question 33

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

Answer 33

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.

Question 34

Solve:

Answer 34

You're just left with 20

Question 35

Solve

Answer 35

50

Question 36

Can you log a negative number?

Answer 36

Nope!

Question 37

Solve:

Answer 37

12

Question 38

Solve:

Answer 38

pi

Question 39

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

Answer 39

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.

Question 40

What is the relationship between exponential and logarithmic functions?

Answer 40

Logarithms are the inverse of exponential functions

Question 41

What are 4 facts about logarithms on a graph?

Answer 41

Question 42

Answer 42

Question 43

Answer 43

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

Question 44

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

Answer 44

Question 45

Use transformations to sketch:

Answer 45

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

Question 46

Use transformations to sketch.

Answer 46

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