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Common Core Standard HSF-IF.C.8b Questions

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

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Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
An initial investment of $2,000 is placed in an account with 6% interest compounded annually. What is the function to model this investment after t years?
  1. [math]A(t)=2000(1+0.06)^t[/math]
  2. [math]A(t)=2000(1-0.06)^t[/math]
  3. [math]A(t)=2000(0.06)^(-t[/math]
  4. [math]A(t)=2000(1+0.6)^t[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
The function [math]y=(0.92)^t[/math] represents what percent rate of change, and is it growth or decay?
  1. 8%, decay
  2. 8%, growth
  3. 92%, decay
  4. 92%, growth
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify the function [math]f(x)=(3^x)(9^(x/2)[/math], and determine the percent rate of change.
  1. 9%, decay
  2. 300%, growth
  3. 200%, growth
  4. 100%, decay
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify the function [math]f(x) = (2^x)(4^x)[/math] and determine the percent rate of change.
  1. [math]f(x) = 2^(2x), 100% growth [/math]
  2. [math]f(x) = 8^(x), 700% growth [/math]
  3. [math]f(x) = 2^(3x), 100% growth [/math]
  4. [math]f(x) = 4^(2x), 400% growth [/math]
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify the function [math]f(x) = (2^x)(4^(-x/2)[/math] and identify the rate of change.
  1. 25%, growth
  2. 75%, decay
  3. 25%, decay
  4. None of the above
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
Which of the following functions represents exponential decay?
  1. [math]y=(1.04)^t[/math]
  2. [math]y=(0.98)^t[/math]
  3. [math]y=(1.01)^t[/math]
  4. [math]y=(1.05)^t[/math]
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify [math]f(x)=(3^x)(9^x)[/math], and determine the rate of change.
  1. 9%, decay
  2. 900%, growth
  3. 1200%, growth
  4. 200%, growth
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
An investment of $5,000 earns 4% interest compounded quarterly. What is the function to model the value of the investment after t years?
  1. [math]A(t)=5000(1+0.04)^t[/math]
  2. [math]A(t)=5000(1+0.04/4)^(4t[/math]
  3. [math]A(t)=5000(1+0.04/12)^(12t[/math]
  4. [math]A(t)=5000(1+0.04)^4[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify the function [math]f(x)=(2^x)(64^(-x/2)[/math], and identify the rate of change.
  1. 200%, decay
  2. 100%, growth
  3. 50%, growth
  4. 100%, decay
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify the function [math]g(x) = (3^x)/(9^x)[/math] and determine if it represents growth or decay.
  1. [math]g(x) = 3^(-x), decay [/math]
  2. [math]g(x) = 1/3^(x), decay [/math]
  3. [math]g(x) = 3^(2x), decay [/math]
  4. [math]g(x) = 1/9^(x), decay [/math]
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
An initial investment of $10,000 earns 8% interest compounded annually. What is the function to model the investment after t years?
  1. [math]A(t) = 10000(1 + 0.08)^t[/math]
  2. [math]A(t) = 10000(1 - 0.08)^t[/math]
  3. [math]A(t) = 10000(1 + 0.8)^t[/math]
  4. [math]A(t) = 10000(0.08)^t[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.C.8, HSF-IF.C.8b
Which of the following functions represents a 1% decay per unit time?
  1. [math]y = (1.01)^t[/math]
  2. [math]y = (0.99)^t[/math]
  3. [math]y = (0.01)^t[/math]
  4. [math]y = (1.1)^t[/math]
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
Simplify [math]f(x)=(2^x)(8^(x/3))[/math], and determine the growth rate.
  1. 50%, growth
  2. 100%, growth
  3. 200%, growth
  4. 300%, growth
Grade 11 Exponents CCSS: HSF-IF.C.8, HSF-IF.C.8b
If an initial investment of $5,000 earns 6% interest compounded monthly, what is the function to model this situation?
  1. [math]A(t)=5000(1+0.06/12)^(12t[/math]
  2. [math]A(t)=5000(1-0.06/12)^(12t[/math]
  3. [math]A(t)=5000(1+0.6)^(12t[/math]
  4. [math]A(t)=5000(1+0.06/6)^(12t[/math]
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