Question

Does each equation represent exponential decay or exponential growth?

Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
Exponential Decay Exponential Growth

options:
H=5.9 (0.82)^t
y=0.8 (3.6)^t
f(t)=0.72 (15)^t
A=4/9 (8)^t
A= (4/3)^t
H= 7/2 (5/6)^t
g(x)= 0.3(x)

Answer 1

Are exponential growth function.becauese growth factor is greater than one

`y=9/11(4)^t`

`P=7/9(5/4)^t`

`V=0.8(9)^t`

`P=0.9(8.3)^t`

So function:

`A=(0.97)^t` and
`y=3.7(0.2)^t` are exponential decaying function.

Mathematical concepts known as exponential growth and decay are used to explain how a quantity's value changes over time.

A quantity experiences exponential growth when its value rises by a predetermined percentage over a predetermined amount of time.

Conversely, exponential decay happens when a quantity's value drops by a predetermined percentage over a predetermined amount of time.

An exponential growth function often takes the following form:

`y = ab^x`

where y is the quantity's value at time x,

an is the quantity's starting value,

B is the factor of growth.

The quantity's value is increasing with time, as indicated by the growth factor being greater than 1.

An exponential decay function generally takes the following form:

`y = ab^x`

where

a denotes the quantity's initial value and y is its value at time x.

The factor of decay is b.

The quantity's value is decreasing over time, as shown by the decay factor, which ranges from 0 to 1.

Given function;

`A=(0.97)^t`

`y=3.7(0.2)^t`

`y=9/11(4)^t`

`P=7/9(5/4)^t`

`V=0.8(9)^t`

`P=0.9(8.3)^t`

g(x)=2.1(x) is a linear equation and is not an exponential growth or decay function.

For Exponential growth function:The growth factor is greater than 1, indicating that the value of the quantity is increasing over time.

So, function:

`y=9/11(4)^t`

`P=7/9(5/4)^t`

`V=0.8(9)^t`

`P=0.9(8.3)^t`

Functions of exponential growth. since the growth factor exceeds one

For the function of exponential decay:

The quantity's value is decreasing over time, as shown by the decay factor, which ranges from 0 to 1.

So function:
`A=(0.97)^t` and
`y=3.7(0.2)^t` are exponential decaying function.

Answer 2

A graph will be growing if its exponent is >1. If the exponent is <1 then it would decay. The graph will show a equation of f(x)= i *(r)^t

H=5.9 (0.82)^t ---->0.82 = exponential decay
y=0.8 (3.6)^t ---->3.6 = exponential growth
f(t)=0.72 (15)^t ---->15 = exponential growth
A=4/9 (8)^t ---->8 = exponential growth
A= (4/3)^t ---->4/3 = exponential growth
H= 7/2 (5/6)^t ----> 5/6= exponential decay
g(x)= 0.3(x) ----> no exponent?