14. Exponentials and Logarithms

Question 1

What is an exponential function

Answer 1

f ( x ) = a (to the power of x)
x = index / power / exponent
x axis is an asymptote to the curve

Question 2

How do you treat y = e (to the power of x)?

Answer 2

Graphs of their gradient functions are similar to the shapes of the exponential function
y = e to the x
dy/dx = e to the x
When you differentiate, the power stays the same

Question 3

What are the rules of logarithms?

Answer 3

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Question 4

How does the line of y = e (to the x) link to the line of y = ln x?

Answer 4

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Question 5

How can logarithms be used to explore non-linear trends?

Answer 5

Start with non-linear relationship
Take logs of both sides
Simplify using the laws of logarithms
Compare the equation to y = mx + c (a straight line)

Question 6

What are the two different types of lograithms? How do they differ when using them to explore non-linear trends?

Answer 6

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Question 7

What does the graph of y = 2(to the power of x) look like?

Answer 7

Crosses at (0, 1)
X axis is an asymptote