Lesson 8 Cafeteria Consumption and Cost Develop Understanding

Ready

For each of the given functions, either explicit or recursive, find the missing values in the tables. Use the explicit equations as a tool to find the values. If you are not given the explicit equation, you might consider creating it to help you with your work.

1.

$f (x) = - 2 x + 7$

$x$	$f (x)$
$- 3$
$0$
	$43$
$21$

2.

$g (x) = 3 x - 25$

$x$	$g (x)$
$- 8$
	$26$
$12$
	$- 37$

3.

$h (n) = h (n - 1) + 6; h (1) = - 13$

$n$	$h (n)$
$3$
$15$
	$5$
	$23$

4.

$d (t) = d (t - 1) - 2; d (1) = 34$

$x$	$d (x)$
$2$
	$- 2$
$10$
	$10$

5.

$y = 7 x - 35$

$x$	$y$
$- 2$
$0$
	$21$
	$0$

6.

$x + y = 24$

$x$	$y$
$10$
	$0$
	$- 20$
$0$

Set

Elvira has been running a private catering business to make extra money. She needs some help organizing the information in problems 7-10 so she can better predict amounts to purchase and improve her profits. Assist her by organizing the information in a meaningful way so she can average the years and do better for the coming year.

7.

The last three years, Elvira has catered family gatherings and city events. Last year, she provided the following at family gatherings she catered: $5$ bags of chips, $6$ dozen cookies, and $4$ gallons of drink. Last year at city events she provided the following: $16$ bags of chips, $20$ gallons of drink, and $24$ dozen cookies. Organize this information.

8.

Two years ago, Elvira provided the following at family events: $5$ gallons of drink, $4$ bags of chips, and $5$ dozen cookies. While she provided the following at city events: $20$ dozen cookies, $18$ gallons of drink, and $12$ bags of chips.

9.

Three years ago, Elvira provided the following at city events: $14$ bags of chips, $20$ gallons of drink, and $19$ dozen cookies. She also provided the following at family gatherings: $6$ bags of chips, $7$ dozen cookies, and $9$ gallons of drink.

10.

If you provide Elvira with an average amount to be ordered for the gatherings and events she caters in the coming year, how much of each item would she need? Present the average in an organized way. Round your answers up so that Elvira knows she will have enough.

Go

Remember sequences from the beginning of the year. For each sequence given, determine whether it is arithmetic or geometric and find both the recursive and the explicit equations.

11.

$1, 3, 5, 7, \dots$

Arithmetic or Geometric?

Recursive:

Explicit:

12.

$3, 6, 12, 24, \dots$

Arithmetic or Geometric?

Recursive:

Explicit:

13.

Time (in days)	Number of People
$1$	$3$
$2$	$7$
$3$	$11$
$4$	$15$

Arithmetic or Geometric?

Recursive:

Explicit:

14.

Time (in days)	Number of Bacteria
$1$	$5$
$2$	$8$
$3$	$12.8$
$4$	$20.48$

Arithmetic or Geometric?

Recursive:

Explicit:

15.

Elvira likes to exercise in her spare time. She has been running. The first days she went running, she did $1,000$ yards. She has been running an additional $50$ yards each day she works out.

Arithmetic or Geometric?

Recursive:

Explicit:

16.

Evan has started a business and, following Bill’s example, is going to send out a chain email to get customers. He sends the email to $5$ people the first day, and they each are going to send it to $7$ people. Then, those $7$ people will each send it to $7$ more and so on.

Arithmetic or Geometric?

Recursive:

Explicit: