Algebra 1 Common Core Student Edition, Grade 8-9

40. C om pare th e rule an d th e function table below. W hich function h as th e greater
    value w h en x = 12? Explain.
    Function 1

y = 4X

F u n ctio n 2

X 1 234

y^525125625

Hydra

41. You have ju st read a journal article ab o u t a p o p u latio n of fungi th a t doubles every

3 weeks. The beginning p o p u latio n was 10. The function y = 10 • 7? represents the

p o pulation after n w e e k s.

a. You have a p o p u latio n of 15 of th e sam e fungi. A ssum ing th e journal articles

gives th e correct rate of increase, w rite th e function th a t represents the

p o pulation of fungi after n w e e k s.

b. Suppose you find a n o th er article th a t states th a t th e fungi p o p u latio n triples

every 4 weeks. If th ere are currently 15 fungi in your population, w rite the

function th at represents th e p o p u latio n after n w e e k s.

42. Think About a Plan Hydra are small freshw ater anim als. They
    can double in n u m b e r every two days in a laboratory tank.
    Suppose one tan k has an initial p o pulation of 60 hydra.
    W hen will there be m ore th a n 5000 hydra?

• How can a table help you identify a pattern?


• W hat function m odels th e situation?

43. a. Graph y = 2X, y = 4X, a n d y = 0.25x on th e sam e axes.
    b. W hat p o in t is on all three graphs?
    c. Does th e graph of an exponential function intersect th e x-axis?
    Explain.
    d. Reasoning How does th e graph of y = b x change as th e b ase b
    increases or decreases?

Which function has the greater value for the given value of x?

44. y = 4X o r y = x 4 for x = 2 45. f(x) = 10 • 2* or / ( x ) = 200 • x 2 for x = 7


45. y = 3X or y = x 3 for x = 5 47. /(x) = 2X or /( x ) = 100x2 for x = 10


46. Computers A co m p u ter valued at $1500 loses 20% of its value each year.
    a. Write a function rule th a t m odels th e value of th e com puter.
    b. Find th e value of th e com puter after 3 yr.
    c. In how m any years will th e value of th e co m p u ter be less th a n $500?
    rj 49. a. G raph th e functions y = x 2 an d y = 2* on the sam e axes.
    “ b. W hat do you notice ab o u t th e graphs for th e values of x betw een 1 an d 3?
    c. R e a so n in g How do you th in k th e graph of y = 8X w ould com pare to th e graphs
    of y = x 2 an d y = 2X?


47. W riting Find the range of th e function /(x ) = 500 • lx using th e dom ain
    {1, 2,3, 4, 5 }. Explain why the definition of exponential function states th a t b # 1.

458 Chapter 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s