4/16 Alg1 Review: Exponential Functions

Initial Amount/Constant Ratio

100

What is the constant ratio of the function?

f(x) = 3^x

3

200

What is the initial amount of the function?

f(x) = 3(9)^x

3

300

What is the initial amount of the function?

f(x) = (1/2)^x

1

400

Identify both the constant ratio and the initial amount of the function. 

f(x) = 8(1.2)^x

Constant ratio: 1.2

Initial amount: 8

Increasing or Decreasing?

100

See slide 20

Decreasing.

200

f(x) = 6(1/4)^x

Decreasing

300

The exponential function f(x)=2^x increases as x increases. Do all exponential functions of the form b^x behave this way?

No. Exponential functions decrease when 0<b<1.

400

f(x) = b^x, where b = 1.

NEITHER! It is constant. 

Write a Function

100

See slide 21.

f(x) = 5(2)^x

200

(0, 20) 

(1, 10)

(2, 5)

(3, 5/2)

(4, 5/4)

f(x) = 20(1/2)^x

300

Identify the error Ms. K made when writing the function with the following characteristics. 

Initial Amount: 6

Constant Ratio: 1/3

f(x) = 6(1/3)^x

f(x) = 2^x

She multiplied the initial amount and constant ratio, which is mathematically incorrect according to the rules of exponents and multiplication. 

400

See slide 22.

f(x) = 3(2)^x

Linear or Exponential?

100

All functions of the general form y = mx + b

Linear

200

All functions of the general form f(x) = a(b)^x

Exponential

300

See slide 23.

Linear

400

Scientists have discovered a new species of rabbits. When studying the population of rabbits over time, the scientists observe that the population of rabbits doubles every 3 months. 

Exponential