For Exercises 51-52, estimate the value of each logarithm between two consecutive integers. Then use a calculator to approximate the value to 4 decimal places. For example, log 8970 is between 3 and 4 because 10 3 < 8970 < 10 4 . (See Example 5 ) a . log 46 , 832 b . log 1 , 247 , 310 c . log 0.24 d . log 0.0000032 e . log 5.6 × 10 5 f . log 5.1 × 10 − 3
For Exercises 51-52, estimate the value of each logarithm between two consecutive integers. Then use a calculator to approximate the value to 4 decimal places. For example, log 8970 is between 3 and 4 because 10 3 < 8970 < 10 4 . (See Example 5 ) a . log 46 , 832 b . log 1 , 247 , 310 c . log 0.24 d . log 0.0000032 e . log 5.6 × 10 5 f . log 5.1 × 10 − 3
Solution Summary: The author explains the value of mathrmlog46,832 between two consecutive integers, and uses the TI-83 graphing calculator to approximate it.
For Exercises 51-52, estimate the value of each logarithm between two consecutive integers. Then use a calculator to approximate the value to 4 decimal places. For example,
log
8970
is between 3 and 4 because
10
3
<
8970
<
10
4
.
(See Example 5)
a
.
log
46
,
832
b
.
log
1
,
247
,
310
c
.
log
0.24
d
.
log
0.0000032
e
.
log
5.6
×
10
5
f
.
log
5.1
×
10
−
3
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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