Chapter 8

17. The doubling function y 5 y 0 2 t D
can be used to model exponential
T
growth when the doubling time is D. The bacterium Escherichia coli
has a doubling period of 0.32 h. A culture of E. coli starts with
100 bacteria.
a) Determine the equation for the number of bacteria, y, in x hours.
b) Graph your equation.
c) Graph the inverse.
d) Determine the equation of the inverse. What does this equation
represent?
e) How many hours will it take for there to be 450 bacteria in the
culture? Explain your strategy.
18. To evaluate a logarithm whose base is not 10 you can use the
following relationship (which will be developed in section 8.5):
log a b 5 log b
log a
Use this to evaluate each of the following to four decimal places.
a) log 5 5
c) log 5 45
e) log 4 0.5
b) log 2 10
d) log 8 92
f) log 7 325
19. Consider the expression log 5 a.
C
a) For what values of a will this expression yield positive numbers?
b) For what values of a will this expression yield negative numbers?
c) For what values of a will this expression be undefined?
Extending
20. Simplify.
3 log327 1 10 log 101000
a) b)
5 log 58 2 3 log 351log 3 7
21. Determine the inverse of each relation.
a) y 5 " 3 x
c) y 5 (0.5) x12
b) y 5 3(2) x d) y 5 3 log 2 (x 2 3) 1 2
22. Graph each function and its inverse. State the domain, range, and
asymptote of each. Determine the equation of the inverse.
a) y 5 3 log (x 1 6) d) y 5 20(8) x
b) y 522 log 5 3x e) y 5 2(3) x12
c) y 5 2 1 3 log x f) y 525 x 2 3
23. For the function y 5 log 10 x, where 0 , x , 1000, how many integer
values of y are possible if y .220?
468 8.3 Evaluating Logarithms
NEL