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