Algebra 1 Common Core Student Edition, Grade 8-9

^ Challenge 32. Forestry A forester plants a tree a n d m easures its circum ference yearly over the

r next four years. The table shows th e forester’s m easurem ents.

r— .....-............................... ^

Tree G row th

Time (yr) 1 2 3 4

Circumference (in.) 24 6 8

a. Show th a t th e d ata are linear, an d write an equation th a t m odels the data.

b. Predict the circumference of the tree after 10 yr.

c. The circum ference of th e tree after 10 yr was actually 43 in. After four m ore

years, the circum ference was 49 in. Based on this n ew inform ation, does the

relationship b etw een tim e an d circum ference continue to b e linear? Explain.

MP 2, M P 4

In th e Apply W hat You’ve Learned in Lesson 5-1, you show ed th a t there is a

linear relationship betw een the n u m b e r of m arbles in th e glass on page 293 an d

the height of th e water.

a. Choose two points from th e table at th e right, w hich shows

th e height of th e w ater in the glass w h en different n u m b ers

of m arbles are dro p p ed into it. Use the points to write an

equ atio n in slope-intercept form th at gives the w ater height

y as a function of th e n u m b e r of m arbles x in th e glass.

b. W hat does th e y-intercept of th e graph of your equ atio n

represent? W hat does th e slope represent?

c. Evaluate the function from p a rt (a) w h en x = 40. Does the

w ater height given by the function m ake sense? Explain.

W hat does the function value tell you ab o u t w h at w ould

h a p p e n if you d ro p p ed 40 m arbles in the glass?

[ Number of

1 M a r b l e s , x

Height of

Water (cm), y 1

3 6.9

5 7.5

9 8.7

14 10.2

(^17) 11.1
(^23) ,2 .9
3 2 0 Chap t er 5 Linear Funct ions