An exponential model can be described by the function 

where: a is the initial population or the starting number, b is the base and x is the number of periods elapsed.
When the base of an exponential model is greater than 1 it is called a growth factor, but when it is less than 1 it is called a decay factor.
Given the exponential model 

n is the final output of the exponential model, 20.5 is the starting number, 0.6394 is the base and t is the number of periods/time elapsed.
Here, the base is 0.6394 which is less than 1, hence a decay factor.
Therefore, <span>the
base, b, of the exponential model is 0.6394; It is a
decay factor.</span>
 
        
        
        
Answer:
10x
Step-by-step explanation:
 
        
             
        
        
        
X=number of bottles sold by Sammy.
y=number of bottles sold by David.
We can suggest the following system of equations:
x/y=5/3
x+y=160
We solve the system of equations by substitution method.
x+y=160        ⇒y=160-x
x/(160-x)=5/3
3x=5(160-x)
3x=800-5x
3x+5x=800
8x=800
x=800/8
x=100
y=160-x
y=160-100
y=60
answer: Sammy sold 100 bottles and David sold 60 bottles.
other method.
5x=bottles sold by Sammy
3x=bottles sold by David.
We can suggest the following equation:
5x+3x=160
8x=160
x=160/8
x=20
bottles sold by Sammy: 5x=5(20)=100
bottles sold by David:  3x=3(20)=60
Answer:Sammy sold 100 bottles and David sold 60 bottles. 
        
             
        
        
        
The equation that can be used to represent the area of the triangle is A(x) = 0.5(f ∙ g)(x) ⇒ 2nd answer
Step-by-step explanation:
The formula of the area of a triangle is A =  b h, where
 b h, where
- b is the length of the base of the triangle
- h is the length of the height of the triangle
∵ The area of the triangle when x = 2 is 14
∴ The base and the height of the triangle are functions of x
Assume that the length of the base of the triangle is represented by f(x) and the length of the height of the triangle is represented by g(x)
∵ A = =  b h
 b h
∵ b = f(x)
∵ h = g(x)
- Substitute b by f(x) and h by g(x) in the rule and replace A by
    A(x) because the area of the triangle is a function of x 
∴ A(x) =  f(x) . g(x)
 f(x) . g(x)
∵ f(x) . g(x) can be written as (f . g)(x)
∴ A =  (f . g)(x)
 (f . g)(x)
∵   = 0.5
  = 0.5
∴ A = 0.5(f . g)(x)
The equation that can be used to represent the area of the triangle is A(x) = 0.5(f ∙ g)(x)
Learn more:
You can learn more about the functions in brainly.com/question/2645523
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