Carbon Dating The age in years of a specimen that originally contained 10 grams of carbon 14 is given by y = log 0.999879 ( 0.1 x ) , where x is the amount of carbon 14 it currently contains Compute. d y d x | x = 5 , and interpret your answer. [ HINT: For the calculation, see Quick Examples 3 and 4.]
Carbon Dating The age in years of a specimen that originally contained 10 grams of carbon 14 is given by y = log 0.999879 ( 0.1 x ) , where x is the amount of carbon 14 it currently contains Compute. d y d x | x = 5 , and interpret your answer. [ HINT: For the calculation, see Quick Examples 3 and 4.]
Solution Summary: The author analyzes the function y=mathrmlog_0.999879(0.1x), where x represents the amount of carbon 14 contained by the specimen
Carbon Dating The age in years of a specimen that originally contained 10 grams of carbon 14 is given by
y
=
log
0.999879
(
0.1
x
)
,
where x is the amount of carbon 14 it currently contains Compute.
d
y
d
x
|
x
=
5
, and interpret your answer. [HINT: For the calculation, see Quick Examples 3 and 4.]
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Chapter 11 Solutions
Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th
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