Question

HELPPPPPPPPPPP WITH CACULAS

Answer 1

These are four questions and four answers:

Question 1. What is the petrochemical production in 2005?

Solution:

1) The table reports the the annual Petrochemical Production p (Billion metric tons) for 2005 - 2011.

2) The years are indicated as 0, 1, 2, 3, 4, 5, 6.

3) There is a contradiction in the stament because there is a note telling that t = 0 is year 2002, which meant that the years are from 2002 - 2008, contradicting that the years are 2005 - 2011.

4) If you take for good the note the t = 3 is year 2005 and the corresponding production is 12.0, which is the option A).

5) If you take for good the initial statement that the years are 2005 - 2011, then t = 0 is 2005 and the corresponding production is 10.8

So you have to clarify with your teacher which is the right statement.

Question 2. What are the units.

Solution:

The units are indicated in parenthesis after the label of the row.

The label of the row is Petrochemical production p and the units are Billion metric tons.

So, the answer is the option D) billion metric tons.

Question 3. Graph the function f(x) = log base 2 of x

Solution:

You might create a table with some four points or use the knowledge about logarithm function.

Thiis is the knowledge you need to answer the question:

1) logarithm is an increasing function: as x increase f(x) increase)

2) log base a of a = 1

3) limit of log base a of x when x approaches 0 is negative infinity.

With those three properties you know that the answer is the first figure with certainty.

Question 4. Graph the function f(x) = 2^x

Solution:
 
These properties will give you the answer:

1) 2^x is the inverse function of log base 2 of x (the function of the question 2)

2) 2^0 = 1

3) 2^x is a growing function (as x increases 2^x increases)

4) 2^x is always positive.

5) limit of 2^x when x approaches negative infinity is 0.

With that you are sure that the graph of 2^x is the second figure.