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