Thomas Calculus 13th [Solutions]

34 Chapter 1 Functions
35. After t hours, the population is
48 14
P(24) 2 2.815 10 bacteria.
t/0.5
P( t ) 2 , or equivalently,
2t
P( t ) 2 . After 24 hours, the population is
36. (a) Each year, the number of cases is 100% 20% = 80% of the previous years number of cases. After
t years, the number of cases will be C( t )
t
10,000(0.8) . Solving C(t) = 1000 graphically, we find that
t 10.319. It will take 10.319 years.
(b) Solving C(t) = 1 graphically, we find that t 41.275. It will take about 41.275 years.
1.6 INVERSE FUNCTIONS AND LOGARITHMS
1. Yes one-to-one, the graph passes the horizontal line test.
2. Not one-to-one, the graph fails the horizontal line test.
3. Not one-to-one since (for example) the horizontal line y = 2 intersects the graph twice.
4. Not one-to-one, the graph fails the horizontal line test.
5. Yes one-to-one, the graph passes the horizontal line test.
6. Yes one-to-one, the graph passes the horizontal line test.
7. Not one-to-one since the horizontal line y = 3 intersects the graph an infinite number of times.
8. Yes one-to-one, the graph passes the horizontal line test.
9. Yes one-to one, graph passes the horizontal line test.
10. Not one-to-one since (for example) the horizontal line y = 1 intersects the graph twice.
11. Domain: 0 < x 1, Range: 0 y 12. Domain: x < 1, Range: y > 0
13. Domain: 1 x 1, Range:
y 14. Domain: < x < , Range:
2 2
y
2 2
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