Writing Equations for Exponential Functions

Writing Equations for Exponential Functions

f(x) = a(b)^x

• a: y-intercept

• b: base or common ratio

f(x) = 5(2)^x

• y-intercept: (0,5)

• base/common ratio: 2

Multiple Choice

What is the y-intercept and base of f(x) = 4(2)^x ?

• y-int: (0,4)
  
  base: 2

• y-int: (4,0)
  
  base: 2

• y-int: (2,0)
  
  base: 4

• y-int: (0,2)
  
  base: 4

Multiple Choice

What is the y-intercept and base of f(x) = 8( $\frac{3}{4}$ )^x ?

• y-int: (0,3/4)
  
  base: 8

• y-int: (0,8)
  
  base: 3/4

• y-int: (8,0)
  
  base: 3/4

• y-int: (3/4,0)
  
  base: 8

Multiple Choice

What is the y-intercept and base of f(x) =  $\frac{5}{2}$  (3)^x ?

• y-int: (0,3)
  
  base: 5/2

• y-int: (3,0)
  
  base: 5/2

• y-int: (5/2,0)
  
  base: 3

• y-int: (0,5/2)
  
  base: 3

Multiple Choice

Given the y-intercept and base of an exponential function, identify the equation that represents it.

y-int: (0,1)

base: 2.5

• f(x) = 2.5x + 1

• f(x) = 1x + 2.5

• f(x) = 1(2.5)^x

• f(x)= 2.5(1)^x

Multiple Choice

Given the y-intercept and base of an exponential function, identify the equation that represents it.

y-int: (0,1/2)

base: 3

• f(x) = $3\left(\frac{1}{2}\right)^x$

• f(x) = $\frac{1}{2}\left(3\right)^x$

• f(x) = $3x+\frac{1}{2}$

• f(x)= $\frac{1}{2}x+3$

Multiple Choice

Given the y-intercept and base of an exponential function, identify the equation that represents it.

y-int: (0,9)

base: 2

• f(x) = $9\left(2\right)^x$ 

• f(x) =  $9x+2$ 

• f(x) =  2x + 9

• f(x)=  $2\left(9\right)^x$ 

Multiple Choice

Given the y-intercept and base of an exponential function, identify the equation that represents it.

y-int: (0,4)

base: 3

• f(x) = $3\left(4\right)^x$ 

• f(x) =  $4x+3$ 

• f(x) =  3x + 4

• f(x)=  $4\left(3\right)^x$