Exponentials and Logarithms

Question 1

describe graph of y = a^x?

Answer 1

gradual increase to y-intercept then huge increase per each unit of x. asymptote at y=0

Question 2

describe graph of y = a^x?

Answer 2

gradual increase to y-intercept then huge increase per each unit of x. asymptote at y=0

Question 3

differentiate f(x) = e^kx

Answer 3

f’(x) = ke^kx

Question 4

why can e^x be useful in many applications?

Answer 4

The rate of increase is proportional to the size at any given moment

Question 5

What is loga(n) = x equal to?

Answer 5

a^x=n where a is not equal to 1

Question 6

What is the multiplication law?

Answer 6

loga(x) + loga(y) = loga(xy)

Question 7

What is the division law?

Answer 7

loga(x) - loga(y) = loga(x/y)

Question 8

What is the power law?

Answer 8

loga(x^k) = kloga(x)

Question 9

What is the power law when k = -1?

Answer 9

loga(x^-1) = -loga(x)

Question 10

what does loga(a) equal (when a > 0 and a not equal to one)?

Answer 10

1

Question 11

what does loga(1) equal (when a > 0 and a not equal to one)?

Answer 11

0

Question 12

how are the graphs y=e^x and y=lnx related to one another?

Answer 12

They are reflections in the line y=x