File EditneView History BookmarksPeople Window Help40%Thu Sep 26 10:32 PMM Activity Digest sir Xp MATH 102 ALL (1xE Target Reading 3 XWatch Euphoria XUBCOSH2Desmos Graphi xXUBC LFS-100-LEAP-XX G first principles -xcanvas.ubc.ca/courses/44898/assignments/353927網頁快訊圖庫Imported From IEMathESL English as a...CHEMISTRY LIFE..E Money SpentTV UBC whO0pXDQuestion 1: ForagingBears search for berries that grow in patches that can be spread out across a large area. A bear will spend time in onepatch gathering food before moving to another patch. The number of berries collected in a patch depends on theamount of time spent in the patch: B(t) = Awhere B(t) is the number of berries collected at the end of t hoursk+tnspent in the patch. The constants A and k are positive, and n is a positive constant. The values of A, n, and k vary fordifferent bears and different patches.1a. Suppose a particular patch has 1,000 berries, and it takes the bear one hour to collect 500 berries. Which of theconstants (A. k. and n) can you determine from this information, and what are they? Explain how you got your answer.1b. Suppose a particular bear likes to settle into a berry patch before it really starts eating. So, when it first reaches a0), its rate of berry finding is approximately zero. What does this tell you about the value of n?patch (when t= 1 for arbitrary A and k. (Your answer should depend1c. Using the definition of the derivative, calculate whenndton the unspecified constants A and k, as well as the variable t.)1d. For what values of t is the derivative you calculated positive? negative? What happens to this derivative as time goesto infinity? What do these tell you about the bear's foraging?1e. Relate the difficulty of finding berries to the derivative of B(t). That is, what kinds of derivatives tell you it's toughto find berries, and what kinds of derivatives tell you it's easy?WOPXSEP26

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Asked Sep 27, 2019
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Thu Sep 26 10:32 PM
M Activity Digest sir X
p MATH 102 ALL (1x
E Target Reading 3 X
Watch Euphoria X
UBC
OSH2
Desmos Graphi x
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UBC LFS-100-LEAP-X
X G first principles -x
canvas.ubc.ca/courses/44898/assignments/353927
網頁快訊圖庫
Imported From IE
Math
ESL English as a...
CHEMISTRY LIFE..
E Money Spent
TV UBC whO0p
XD
Question 1: Foraging
Bears search for berries that grow in patches that can be spread out across a large area. A bear will spend time in one
patch gathering food before moving to another patch. The number of berries collected in a patch depends on the
amount of time spent in the patch: B(t) = Awhere B(t) is the number of berries collected at the end of t hours
k+tn
spent in the patch. The constants A and k are positive, and n is a positive constant. The values of A, n, and k vary for
different bears and different patches.
1a. Suppose a particular patch has 1,000 berries, and it takes the bear one hour to collect 500 berries. Which of the
constants (A. k. and n) can you determine from this information, and what are they? Explain how you got your answer.
1b. Suppose a particular bear likes to settle into a berry patch before it really starts eating. So, when it first reaches a
0), its rate of berry finding is approximately zero. What does this tell you about the value of n?
patch (when t
= 1 for arbitrary A and k. (Your answer should depend
1c. Using the definition of the derivative, calculate whenn
dt
on the unspecified constants A and k, as well as the variable t.)
1d. For what values of t is the derivative you calculated positive? negative? What happens to this derivative as time goes
to infinity? What do these tell you about the bear's foraging?
1e. Relate the difficulty of finding berries to the derivative of B(t). That is, what kinds of derivatives tell you it's tough
to find berries, and what kinds of derivatives tell you it's easy?
WOPX
SEP
26
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File Edit ne View History Bookmarks People Window Help 40% Thu Sep 26 10:32 PM M Activity Digest sir X p MATH 102 ALL (1x E Target Reading 3 X Watch Euphoria X UBC OSH2 Desmos Graphi x X UBC LFS-100-LEAP-X X G first principles -x canvas.ubc.ca/courses/44898/assignments/353927 網頁快訊圖庫 Imported From IE Math ESL English as a... CHEMISTRY LIFE.. E Money Spent TV UBC whO0p XD Question 1: Foraging Bears search for berries that grow in patches that can be spread out across a large area. A bear will spend time in one patch gathering food before moving to another patch. The number of berries collected in a patch depends on the amount of time spent in the patch: B(t) = Awhere B(t) is the number of berries collected at the end of t hours k+tn spent in the patch. The constants A and k are positive, and n is a positive constant. The values of A, n, and k vary for different bears and different patches. 1a. Suppose a particular patch has 1,000 berries, and it takes the bear one hour to collect 500 berries. Which of the constants (A. k. and n) can you determine from this information, and what are they? Explain how you got your answer. 1b. Suppose a particular bear likes to settle into a berry patch before it really starts eating. So, when it first reaches a 0), its rate of berry finding is approximately zero. What does this tell you about the value of n? patch (when t = 1 for arbitrary A and k. (Your answer should depend 1c. Using the definition of the derivative, calculate whenn dt on the unspecified constants A and k, as well as the variable t.) 1d. For what values of t is the derivative you calculated positive? negative? What happens to this derivative as time goes to infinity? What do these tell you about the bear's foraging? 1e. Relate the difficulty of finding berries to the derivative of B(t). That is, what kinds of derivatives tell you it's tough to find berries, and what kinds of derivatives tell you it's easy? WOPX SEP 26

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Expert Answer

Step 1

Hello. Since your question has multiple sub-parts, so as per guidelines we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the question and specify those sub-parts you want us to solve.

Now, come to question:

According to the information available the number of berries collected in a patch depends upon the amount of time spent in the patch and is given by:

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At" B (t) K+t" where B(t is the number of berries collected at the end oft hours

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Step 2

For 1(a), the information provided:

The number of berries collected is 1000 and time is given to be 2 hours.

So, only A can be determined from this information:

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Step 3

SO, as n approaches to infinity, one...

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as n K 1000 +1 = A 2" A1000(0+1) A 1000

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