Investigation Additional Practice. a. b. c. d.,,7 e. n.?.?.?,.?,. a. Color Branches 9 7 79 b. b c c. Color 7 would be used to draw,7 branches. d. Branching Pattern Branches Color Skill: Using Eponents...7......;...7.7; 7.9 7. ;....;. 9... 9...7..7 Investigation Additional Practice. a. gal. gal/min minutes b. The relationship is linear: w.t, where w is the water the bathtub will hold and t is the time in minutes to fill it.. a. It will take about hours. b. The relationship is eponential: b n, where b is the number of bacteria in the colon and n is the time in hours.. a.? = cans b. The relationship is linear: c l, where c is the number of cans in a laer and l is the number of the laer.. a. On the sith da, the plant will be times its original height. On the nth da, it will be n times its original height. b. centimeter tall c. The relationship is eponential: c ( n ), where c is the current height and n is the da of the eperiment.. linear; 7. eponential; ( ) or 7. eponential; ( ) or ( ). inverse; 9. neither linear nor eponential Skill: Eponential Functions. r r r r r r r Value of Investment $ $ $ $7 $ $7 $9. $,.7
.. mo mo 9 mo mo mo mo mo Number of Animals 7 7,, Amount of Matter g Investigation Additional Practice. a. about $,79 b. The relationship is eponential: V,(. ), where V is the value and is the number of ears.. a. Balance $,. $,. $,. $,. $,. $,.... r r r r r r 7 r O O g g g, g, g, g, g O b. b,(. t ) c. It will take between ears ($,9) and ears ($,) for the original deposit to double. d. It will take between 7 ears ($,97) and ears ($,7) for the original deposit to double at an interest rate of %. A % interest rate cuts the doubling time approimatel in half.. eponential; (. ). eponential; (.). linear;... inverse; 7. a. 9 7 O
b. All three graphs intersect at the point (, ). If students consider intersections of just two graphs, the graphs of and intersect at about (., 9.). The graphs of and intersect at about (.,.). c. The graph of increases at the greatest rate for between and (about.); then the graph of increases at the greatest rate. d. Because the graph of is a straight line, it is not an eample of eponential growth. e. The equation does not include a variable eponent, so it is not an eample of eponential growth. Skill: Compound Interest. $, $,; $,, $, $,; $,, $7., $,9.; $,9., $7., $,.. $, $7,; $7,, $., $7,.; $7,., $9., $7,7.; $7,7., $., $,.. a.?. ; $. b. $,.7 c. $,7,7.9 d. $,,7. Investigation Additional Practice. a. 7.....7.9.9 b. c. 7 7 7 9 Walking Eercise Walking Eercise 7
d. The first walking eercise is an eample of eponential deca. The walkers get ver close ver fast. The second walking eercise is a linear relationship. The decrease is more gradual and consistent, and it will take longer for them to get close. However, the will meet (or walk past each other); in the eponential situation, theoreticall, the will never meet.. a..9 b. r,(.9t), where r is trees remaining and t is time in ears c. (Figure ) d. This will be when about, of the trees remain, which will occur around ear 7 (when about,99 trees remain). (Note: Students can solve this b trial-and-error or b graphing.) Trees Remaining Figure Tree Harvest, 9,, 7,,,,,,, Trees Remaining,97 Suppl of Trees,,,77. a. b. T,(.7) c. 7 Skill: Eponential Growth and Deca. ; (, ); ; (, ); ; (, );.; (,.);.; (,.) O Tribett Population Tribetts, 7,,9,,,. a.,,?.9;,, b.,7, c.,7, d.,,. a.,?.; $,9 b. $7,. c. $,.7 d. $,7.. a.,9,?.97;,7, b.,99, c.,7, d.,,,,,
. a.,?.; $, b. $7,. c. $,9. d. $,.9 Investigation Additional Practice. a. b. c. d. e. f.. a. b. c. 7 d. 7. a...7....7. O 7 b. All three graphs intersect at the point (, ). If students consider the intersections of just two graphs, the graphs of.7 and. intersect at about the point (.7,.). c. None; as the -value increases, the -value starts to level off in the eponential relationships; in the linear relationship, the decrease remains constant.. a. False, since and 9,9. b. False, since 7 or,. Skill: Simplifing Eponential Epressions. 7. 7. 7.... = 7.. 9. 9.,9.. 9. 7