Chpt. 7, Exponential and Logarithmic Functions

Question 1

exponential function

Answer 1

The general function of an exponential function is y = ab^x, where x is a real number, a does not equal 0, and b does not equal 1. When b is greater than 1, the function models exponential growth with growth factor b. When b is between 1 and 0, the function models exponential decay with decay factor b.

Question 2

exponential growth

Answer 2

Modeled by an exponential function when b is greater than 1.

Question 3

exponential decay

Answer 3

Modeled by an exponential function when b is between 1 and 0.

Question 4

asymptote

Answer 4

A line that a graph approaches as x or y increases in absolute value.

Question 5

growth factor

Answer 5

The variable “b,” when in an exponential function that models exponential growth.

Question 6

decay factor

Answer 6

The variable “b” when in an exponential function that models exponential decay.

Question 7

function to model exponential growth or decay

Answer 7

A(t) = a(1 + r)^t, where:

A = amount after t time periods (or F)
T = number of time periods
a = initial amount
r = rate of growth/decay

Question 8

natural base exponential function

Answer 8

An exponential function with base e. E = 2.71828(infinity). It is a number similar in usage to pi that becomes very important in PreCalc. and Calc.

Question 9

continuously compounded interest

Answer 9

When interest is compounded continuously on principal P, the value A of an account is A = PE^rt.

Question 10

exponential function transformations, from parent:

y = b^x; a = 1

to:

1. stretch
2. compression
3. reflection in x-axis
4. horizontal translation
5. vertical translation
6. all transformations combined

Answer 10

1. y = ab^x; abs. val. of a is > 1
2. y = ab^x; abs. val. of a is 0
3. ab^x; a

Question 11

logarithm

Answer 11

The logarithm base b of a positive number x is defined as log(b)x = y, if and only if x = b^y.

Question 12

logarithmic function

Answer 12

The inverse of an exponential function.

Question 13

common logarithm

Answer 13

A logarithm that uses base 10, and thus are written as log(10)x = y. When logx = y is written, and there is no base for the log, it is assumed that the base is 10.

Question 14

logarithmic scale

Answer 14

A scale that uses the logarithm of a quantity, rather than the quantity itself.

Question 15

logarithmic function transformations, from parent:

y = log(b)_x(); b > 0; b does not equal 1

to:

1. stretch
2. compression
3. reflection in x-axis
4. horizontal translation
5. vertical translation
6. all transformations combined

Answer 15

1. y = (a)log(b)_(x); abs. val. of a is > 1
2. y = (a)log(b)_(x); abs. val. of a is between 1 and 0
3. y = (a)log(b)_x; a is

Question 16

change of base formula

Answer 16

log(b)_(M) =

(log(c)(M)) / (log(c)(b)),

where M, b, and c are all positive numbers, are where neither b nor c equal 1

Question 17

properties of logarithms:

1. product property
2. quotient property
3. power property

Answer 17

1. log(b)(mn) = log(b)(m) + log(b)_(n)
2. log(b)(m/n) = log(b)(m) - log(b)_n)
3. log(b)(m^n) = (n)log(b)(m)

*The above properties apply only when m, n, and b are all positive, and when b does not equal 1.

Question 18

exponential equation

Answer 18

This type of equation is in the form y = b^cx, in which the variable is located in the exponent.

Question 19

logarithmic equation

Answer 19

An equation that includes a logarithm involving a variable. For example, log(3)_(x) = 4.

Question 20

natural logarithmic function

Answer 20

A logarithmic function with base e. The natural logarithmic function, log(E)_(x), can also be written as y = ln(x). It is the inverse of y = e^x. Ln is basically another way of writing log(e).

Question 21

more properties of logarithms;

b^0 = 1, so log(b)(1) =
b^1 = b, so log(b)(b) =
b( log(b)(x) ) = x, so log(b)(b^x) =
b^x(b^y) = b^(x +y), so log(b)_(x/y) =

Answer 21

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