Does each function describe exponential growth or decay?

drag and drop the equations into the boxes to correctly complete the table.

growth decay
y=100(1−12)^t

y=0.1(1.25)^t

y=((1−0.03)12)^2t

y=426(0.98)^t

y=2050(12)^t

A function from a set to a set is a relation that assigns to each element in the set exactly one element in the set . The set is the domain (also called the set of inputs) of the function and the set contains the range (also called the set of outputs).

.

We have the following equation:

That can be written as:

Recall that the definition of exponential functions establishes that:

.

That is:

In this problem, , therefore this is not an exponential function.

The function:

is an exponential function because is a function of the form

So . Since and being raised to the power of , the function increases. This means that increases as increases as illustrated in Figure 1. This represents a growth.

The function:

can be written as:

and is an exponential function because is a function of the form

So . Since and being raised to the power of , the function increases. As in the previous exercise, this means that increases as increases as illustrated in Figure 2. This represents a growth.

The function:

is an exponential function because is a function of the form

So . Since and being raised to the power of , the function decreases. Here this means that decreases as increases as illustrated in Figure 3. This represents a decay.

The function:

is an exponential function because is a function of the form

So . Since and being raised to the power of , the function increases. So in this function also increases as increases as illustrated in Figure 4. This represents a growth.

1. isn't an exponential function

2. growths

3. growths

4. decay

5. growths

Step-by-step explanation:

The exponential functions has the form: y = k1*k2^(k3*t), where k1, k2 and k3 are a constants, and k2>0. Graph of exponential functions always decrease or always increase. To know if a function growths or decay just evaluate the function in 2 points, for example t = 0 and t = 1, and compare their results.

1.

y = 100*(1−12)^x = 100*(−11)^x

Since (-11) is negative, then y is not an exponential function

2.

y(0) = 0.1*(1.25)^(0) = 0.1

y(1) = 0.1*(1.25)^(1) = 0.125

y(1) > y(0) -> growths

3.

y(0) =((1−0.03)12)^2(0) = 1

y(0) =((1−0.03)12)^2(1) = 135.4896

y(1) > y(0) -> growths

4.

y(0) = 426(0.98)^(0) = 426

y(1) = 426(0.98)^(1) = 417.48

y(1) < y(0) -> decay

5.

y(0) = 2050(12)^(0) = 2050

y(1) = 2050(12)^(1) = 24600

y(1) > y(0) -> growths

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: