11 Feb Identify a key concept or foundational theory from the first four weeks of class and in half a page discuss how it applies to your current work environment or a recent social,

SAM WORK

EACH DISCUSSION WRITE IN 150 EACH

MATH110

Discussion 4.1

Identify a key concept or foundational theory from the first four weeks of class and in half a page discuss how it applies to your current work environment or a recent social, political or business event. Include the chapter and sub topic from your textbook.

Discussion 5.1

Two different samples of radioactive isotopes are decaying. The isotopes have initial amounts of c1 and c2 and half-lives of k1 and k2, respectively. Find an expression for the time t required for the samples to decay to equal amounts.

Discussion 5.2

In a classroom designed for 30 students, the air conditioning system can move 450 cubic feet of air per minute.

(a) Determine the ventilation rate per child in a full classroom.

(b) Estimate the air space required per child.

Homework 4 College Algebra (2024) (Homework)

2. Find  f ∘  g, g ∘  f, and   g ∘  g.

f( x) = −3 x,     g( x) =  x + 5

(a)     f ∘  g

(b)     g ∘  f

(c)     g ∘  g

 

 

 

8.  Find the inverse function of  f informally.

f( x) = 2 x

f −1( x) =  

 

 

  Verify that 

f( f −1( x)) =  x

 and 

f −1( f( x)) =  x.

f( f −1( x))	=	f
	=	2
	=	x
f −1( f( x))	=	f −1
	=	2 x
	=	x

 

 

9. Find the inverse function of  f informally.

f( x) = 

1

9

x

f −1( x) =  

 

 

  Verify that 

f( f −1( x)) =  x

 and 

f −1( f( x)) =  x.

f( f −1( x))	=	f
	=	9
	=	x
f −1( f( x))	=	f −1
	=	1 9 x
	=	x

10. Find the inverse function of  f informally.

f( x) = 4 x + 7

f −1( x) =  

 

 

Verify that 

f( f −1( x)) =  x

 and 

f −1( f( x)) =  x.

f( f −1( x))	=	f
	=	4        + 7
	=	x
f −1( f( x))	=	f −1
	=	− 7 4
	=	x

Homework 5 College Algebra (2024) (Homework)

3. Use the One-to-One Property to solve the equation for  x.

2 x + 2 = 8

x = 

4. Use the One-to-One Property to solve the equation for  x.

2 x − 6 = 8

x = 

5. Use the One-to-One Property to solve the equation for  x.

1

4

	x

 = 16

x = 

6. Use the One-to-One Property to solve the equation for  x.

4 x − 5 = 

1

64

 

x = 

7. Write the logarithmic equation in exponential form. For example, the exponential form of 

log5 25 = 2

 is 

52 = 25.

log6 36 = 2

 

8.  Write the logarithmic equation in exponential form. For example, the exponential form of 

log5 25 = 2

 is 

52 = 25.

log9 

1

729

 = −3

 

 9. Evaluate the logarithm at the given value of  x without using a calculator.

Function	Value
f( x) = log2( x)	x = 16

10. Evaluate the logarithm at the given value of  x without using a calculator.

Function	Value
f( x) = log216( x)	x = 6

11. Evaluate the logarithm at the given value of  x without using a calculator.

Function	Value
g( x) = log a( x)	x =  a−3

12. Evaluate the logarithm at the given value of  x without using a calculator.

Function

Value

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