Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Complete the following questions to practice the skills you have learned in this lesson.

Use the following to answer questions 1 – 7.

The table shows values of the expressions $10x^2$ and $2^x$ .

$x$	$10x^2$	$2^x$
$1$	$10$	$2$
$2$	$40$	$4$
$3$	$90$	$8$
$4$	$160$	$16$
$8$
$10$
$12$

Complete the statement.

When the value of $x$ increases by $1$ , the expression $10x^2$ :

Changes logarithmically. It has decreased by one-half.
Grows by decreasing amounts but by increasing growth factors.
Changes exponentially. It doubles.
Grows by increasing amounts but by decreasing growth factors.

When the value of $x$ increases by $1$ , the expression $2^x$ :

Changes logarithmically. It has decreased by one-half.
Grows by decreasing amounts but by increasing growth factors.
Changes exponentially. It doubles.
Grows by increasing amounts but by decreasing growth factors.

Will the value of $10x^2$ be greater than or less than $2^x$ when $x$ is $8$ ?

less than
greater than

Will the value of $2^x$ be greater than or less than $10x^2$ when $x$ is $10$ ?

less than
greater than

Will the value of $10x^2$ be greater than or less than $2^x$ when $x$ is $12$ ?

less than
greater than

Determine the following values of $10x^2$ .

What is the value of $10x^2$ when $x$ is $8$ ?

What is the value of $10x^2$ when $x$ is $10$ ?

What is the value of $10x^2$ when $x$ is $12$ ?

Determine the following values of $2^x$ .

What is the value of $2^x$ when $x$ is $8$ ?

What is the value of $2^x$ when $x$ is $10$ ?

What is the value of $2^x$ when $x$ is $12$ ?

Choose the best statement that describes how the values of the exponential expression $2^x$ and the quadratic expression $10x^2$ change as $x$ becomes greater and greater.

There is no change in the values of the expressions when $x$ increases.
They both grow at the same rate.
The value of the quadratic expression grows much more quickly as $x$ increases.
The value of the exponential expression grows much more quickly as $x$ increases.

Answer the following questions about functions $f(x)$ and $g(x)$ .

What type of expression is $f(x)=1.5^x$ ?

linear
quadratic
exponential

What type of expression is $g(x)=500x^2+345x$ ?

linear
quadratic
exponential

The values of which function will eventually be greater for larger and larger values of $x$ ?

Function $g(x)$
Function $f(x)$

The table shows the values of

4^x

and

100x^2

for some values of

x

.

$x$	$4^x$	$100x^2$
$1$	$4$	$100$
$2$	$16$	$400$
$3$	$64$	$900$
$4$	$256$	$1,600$
$5$	$1,024$	$2,500$

Table 7.4.0

Looking at the patterns in the table, choose the best answer to explain why, as the value of $x$ increases, the values of the exponential expression $4^x$ will eventually overtake the values of the quadratic expression $100x^2$ .

The value of $100x^2$ grows by a factor of $x$ every time and the value of $4^x$ grows by different factors.
The value of $100x^2$ grows by different factors and the value of $4^x$ grows by a factor of $x$ every time.
The value of $100x^2$ grows by a factor of 4 every time and the value of $4^x$ grows by different factors.
The value of $100x^2$ grows by different factors and the value of $4^x$ grows by a factor of 4 every time.

7.4.5 Practice