Use a graphing utility and the change-of-base properly to graph y = log 3 x , y = log 25 x , and y = log 100 x in the same viewing rectangle. a. Which graph is on the top in the interval (0,1)? Which is on the bottom? b. Which graph is on the lop in the interval (1, ∞ )? Which is on the bottom? c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using y = log b x where b > 1. Disprove each statement in Exercises 116-120 by a. letting y equal a positive constant of your choice, and b. using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Use a graphing utility and the change-of-base properly to graph y = log 3 x , y = log 25 x , and y = log 100 x in the same viewing rectangle. a. Which graph is on the top in the interval (0,1)? Which is on the bottom? b. Which graph is on the lop in the interval (1, ∞ )? Which is on the bottom? c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using y = log b x where b > 1. Disprove each statement in Exercises 116-120 by a. letting y equal a positive constant of your choice, and b. using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Solution Summary: The author explains the base-change property for logarithmic functions, which is mathematically expressed as mathrmlog_ba=
Use a graphing utility and the change-of-base properly to graph
y
=
log
3
x
,
y
=
log
25
x
, and
y
=
log
100
x
in the same viewing rectangle.
a. Which graph is on the top in the interval (0,1)? Which is on the bottom?
b. Which graph is on the lop in the interval (1,
∞
)? Which is on the bottom?
c. Generalize by writing a statement about which graph is on top. which is on the bottom, and in which intervals, using
y
=
log
b
x
where b > 1.
Disprove each statement in Exercises 116-120 by
a.letting y equal a positive constant of your choice, and
b.using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs. showing that the equation is not true in general.
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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