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This printable supports Common Core Mathematics Standard HSA-SSE.B.3, HSA-SSE.B.3c

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Rewriting Exponential Expressions (Grades 11-12)

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Rewriting Exponential Expressions

1. 
Rewrite the expression [math]21/(6^(2-2x))[/math] in the form [math]A*B^x[/math].
  1. [math]7/2*1/36^x[/math]
  2. [math]7/2*36^x[/math]
  3. [math]7/12*1/36^x[/math]
  4. [math]7/12*36^x[/math]
2. 
Rewrite the expression [math]2*4^(x+3)*2^(2-x)[/math] in the form [math]A*B^x[/math].
  1. [math]256*2^x[/math]
  2. [math]64*(1/2)^x[/math]
  3. [math]512*2^x[/math]
  4. [math]2*512^x[/math]
3. 
Rewrite the expression [math]6*2^(x-1)*4^(3-x)[/math] in the form [math]A*B^x[/math].
  1. [math]768*(1/2)^x[/math]
  2. [math]192*(1/2)^x[/math]
  3. [math]192*(1/4)^x[/math]
  4. [math]768*2^x[/math]
4. 
Rewrite the expression [math]8*(1/2)^(2x+3)[/math] in the form [math]A*B^x[/math].
  1. [math](1/4)^x[/math]
  2. [math]2*(1/8)^x[/math]
  3. [math]2*(1/4)^x[/math]
  4. [math]8*(1/8)^x[/math]
5. 
Which of the following are equivalent to [math]32*2^(3x)*(1/16)^x ?[/math] Choose all that apply.
  1. [math]2^(3x)*2^x[/math]
  2. [math]2^(5-x)[/math]
  3. [math]32*2^(-x)[/math]
  4. [math]2^(9+7x)[/math]
6. 
Which of the following are equivalent to the expression [math]27*(1+1/9)^(2x) ?[/math] Choose all that apply.
  1. [math]100*3^(3-4x) [/math]
  2. [math]10^(2x) * 3^1[/math]
  3. [math]3^3 *(10/9)^(2x)[/math]
  4. [math]3^(3-4x) * 10^(2x)[/math]
7. 
Which expression is equivalent to [math]8^(2x^2-3x+1)[/math] ?
  1. [math](8^(2x-1))^(x-1)[/math]
  2. [math]16^(x^2-3x+1)[/math]
  3. [math]64^(x^2-3x+1)[/math]
  4. [math]16^(x^2-1x+1)[/math]
8. 
Working with half-life of radioactive isotopes, scientists sometimes use the expression [math]N_0 (1/2)^(t/h)[/math], where [math]N_0[/math] is the original amount of the substance, [math]t[/math] is the time , and [math]h[/math] is the half-life of the substance in question. Rearrange the expression [math]2^((57-5t) \ // \ 19)[/math] to find the approximate half life of RN-222 (in days).
  1. [math]h = 3.8 " days"[/math]
  2. [math]h = 0.3 " days"[/math]
  3. [math]h = 19 " days"[/math]
  4. [math]h = 5 " days"[/math]
9. 
One way exponential growth can be expressed is [math]a(1 + r)^t[/math], where [math]t[/math] represents time, [math]r[/math] is the growth rate, and [math]a[/math] is the initial amount (of the substance or population). If the exponential growth expression is given as [math]5^(3 \ + \ 0.0303t[/math], what is the approximate growth rate?
  1. 105%
  2. 0.05%
  3. 5%
  4. 125%
10. 
Compound interest can be calculated by the expression [math]P(1+r/n)^(nt)[/math], where [math]P[/math] is the initial amount invested, [math]r[/math] is the annual interest rate, [math]n[/math] is the compounding period (the number of times the interest is compounded each year), and [math]t[/math] is the number of years. The expression [math]r/n[/math] gives the interest rate per compounding period. If the expression [math]1.1255^(77.904 \ + \ t)[/math] gives the amount of money in an account that has interest compounded quarterly (four times per year), transform this expression to find the quarterly interest .
  1. [math]60.5%[/math]
  2. [math]50.2%[/math]
  3. [math]12%[/math]
  4. [math]3%[/math]

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