CW 5.3_Exponential Equation

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Mathematics

9th - 12th Grade

CCSS covered

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22 questions

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MATH RESPONSE QUESTION

2 mins • 2 pts

When you solve the following equation, what equation will it be when you have the same bases for both sides? Please type the equation.
(Your answer needs to include the base and the exponents should be simplified.)
$2^{4x+1}=8^{x-5}$

$2^{4x+1}=2^{3x-15}$

Mathematical Equivalence

DROPDOWN QUESTION

1 min • 2 pts

State whether the following functions are examples of exponential growth or decay:
a. $f\left(x\right)=\left(\frac{9}{4}\right)^x$ Exponential (a)
b. $g\left(x\right)=\left(0.87\right)^x$ Exponential (b)

growth

decay

MULTIPLE CHOICE QUESTION

15 mins • 2 pts

Solve the equation: 8^3x+2 = 32³

x=28

x=3

x=1

x=13/2

MATH RESPONSE QUESTION

15 mins • 2 pts

When we solve the equation, we need to change it to be the same bases.
$\left(\frac{1}{16}\right)^{2x+1}=64^{x-3}$
What equation will you get AFTER you have the same bases? Type the equation (your equation should have no bases).

$-4x-2=3x-9$

Mathematical Equivalence

REORDER QUESTION

15 mins • 5 pts

The followings are the steps when we solve the equation below:
$16^{2x-5}=\frac{1}{4}$
Reorder the steps so they are in a correct order.

$4^{-4x+10}=4^{-1}$

$-4x=-11$

$x=\frac{\ 11}{4}$

$-4x+10=-1$

$\left(4^{-2}\right)^{2x-5}=4^{-1}$

MULTIPLE CHOICE QUESTION

15 mins • 2 pts

Solve for b:
4^{3b - 3} = 1/16

-1/4

1/2

1/3

MATCH QUESTION

15 mins • 5 pts

Mathching each group of numbers in exponential form to its equivalent value.

1/9 and 27

$3^{-3}$ and $3^{-4}$

1/25 and 125

$2^2$ and $2^5$

4 and 32

$2^3$ and $2^4$

1/27 and 1/81

$5^{-2}$ and $5^3$

8 and 16

$3^{-2}$ and $3^3$

MATH RESPONSE QUESTION

15 mins • 2 pts

Change the followinge quation with the same bases.
$\left(\frac{1}{2}\right)^{2x-5}=64$
Type the equation with the same bases. (You answer should include the base and the exponents should be simplified.)

$2^{-2x+5}=2^6$

Mathematical Equivalence

MATH RESPONSE QUESTION

10 mins • 2 pts

Solve for x. $5^{3x}=5^{2x-7}$ (Just type the answer without using the equal sign.)

$-7$

Mathematical Equivalence

10.

DROPDOWN QUESTION

10 mins • 1 pt

When you solve the equation: $\frac{1}{125\ }=5^{2x+7}$ , how do yo rewrite the left side of equation? It will be (a)

$5^{-3}$

$-5^3$

$5^{-2}$

$5^{-4}$

$25^{-5}$

$\frac{1}{25^5}$

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CW 5.3_Exponential Equation

When you solve the following equation, what equation will it be when you have the same bases for both sides? Please type the equation.(Your answer needs to include the base and the exponents should be simplified.) 24x+1=8x−52^{4x+1}=8^{x-5}24x+1=8x−5

State whether the following functions are examples of exponential growth or decay:a. f(x)=(94)xf\left(x\right)=\left(\frac{9}{4}\right)^xf(x)=(49​)x Exponential ​ (a) b. g(x)=(0.87)xg\left(x\right)=\left(0.87\right)^xg(x)=(0.87)x Exponential ​ (b)

Solve the equation: 83x+2 = 323

When we solve the equation, we need to change it to be the same bases. (116)2x+1=64x−3\left(\frac{1}{16}\right)^{2x+1}=64^{x-3}(161​)2x+1=64x−3 What equation will you get AFTER you have the same bases? Type the equation (your equation should have no bases).

The followings are the steps when we solve the equation below: 162x−5=1416^{2x-5}=\frac{1}{4}162x−5=41​ Reorder the steps so they are in a correct order.

Solve for b:43b - 3 = 1/16

Mathching each group of numbers in exponential form to its equivalent value.

Change the followinge quation with the same bases. (12)2x−5=64\left(\frac{1}{2}\right)^{2x-5}=64(21​)2x−5=64 Type the equation with the same bases. (You answer should include the base and the exponents should be simplified.)

Solve for x. 53x=52x−75^{3x}=5^{2x-7}53x=52x−7 (Just type the answer without using the equal sign.)

When you solve the equation: 1125 =52x+7\frac{1}{125\ }=5^{2x+7}125 1​=52x+7 , how do yo rewrite the left side of equation? It will be​ (a)

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When you solve the following equation, what equation will it be when you have the same bases for both sides? Please type the equation.
(Your answer needs to include the base and the exponents should be simplified.)
$2^{4x+1}=8^{x-5}$

State whether the following functions are examples of exponential growth or decay:
a. $f\left(x\right)=\left(\frac{9}{4}\right)^x$ Exponential (a)
b. $g\left(x\right)=\left(0.87\right)^x$ Exponential (b)

Solve the equation: 8^3x+2 = 32³

When we solve the equation, we need to change it to be the same bases.
$\left(\frac{1}{16}\right)^{2x+1}=64^{x-3}$
What equation will you get AFTER you have the same bases? Type the equation (your equation should have no bases).

The followings are the steps when we solve the equation below:
$16^{2x-5}=\frac{1}{4}$
Reorder the steps so they are in a correct order.

Solve for b:
4^{3b - 3} = 1/16

Change the followinge quation with the same bases.
$\left(\frac{1}{2}\right)^{2x-5}=64$
Type the equation with the same bases. (You answer should include the base and the exponents should be simplified.)

Solve for x. $5^{3x}=5^{2x-7}$ (Just type the answer without using the equal sign.)

When you solve the equation: $\frac{1}{125\ }=5^{2x+7}$ , how do yo rewrite the left side of equation? It will be (a)