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

2x3 – 6x2 – 14x + 24 square centimeters

if i'm wrong i'm sorry : )

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.