7-5 Rat ional Exponent s and Radicals
Quick Review
If th e nth root of a is a real num ber, m is a n integer, a n d ™ is
in lowest terms, then a* = ffa and a" = 't/a™ = ( f f a )m.Example
Write the expression (8x)s in radical form.
(8x)s = 8^x5 = 2 V xWrite the expression V h 2 as a power with a rational
exponent.
Vb2 = hi
Exercises
Write each expression in radical form,- m*i r--> 5 2. psrs^ i
- (36x4)2 54. (125x)3
5 5. (64)1x1 56. 253i (x2y)^
Write each expression as a power with a rational
exponent.- Vxy 58. V a
- V b 2 60. V x6} '9
- V81x2 62. Vx2y3
7-6 Exponent ial Functions
Quick Review
An exponential function involves re p eated m ultiplication
of an initial a m o u n t a by th e sam e positive n u m b e r b. The
general form of an exponential function is y = a • bx,
where a =f= 0, b > 0, and b + 1.
Example
What is the graph of y = |5?
Make a table of values. G raph th e ordered pairs.an
-2 501-1 101(^012)
(^152)
2
2
Exercises
Evaluate each function for the domain {1,2,3}.
- f{x) = 4*
- y = 4 o ( |) *
Graph each function. - f(x) = 2.5*
- f(x) = | 3
- y = 0.01*
- fix) = 3 2
- y = 0.5(0.5)*
- y = 0.1*
- Biology A p o p u latio n of 50 bacteria in a laboratory
culture doubles every 30 m in. The function
pix) = 50 • 2* m odels th e population, w here x is the
n u m b e r of 30-m in periods.
a. H ow m an y b acteria will th ere be after 2 h?
b. H ow m an y bacteria will th ere be after 1 day?
C
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