Question

The graph shows the deer population in a Pennsylvania county between 2010 and 2014. Assume that the population grows exponentially (8)4 30,000- Deer 20,000 population 10,000 0 1 2 3 4 Years since 2010 (a) What was the deer population in 2010? 20,000 deer (b) Find a function that models the deer population $t$ years after 2010. (Enter your answer in the form $n_0e^{rt}$. Round your $r$ value to four decimal places.) n(t) = (c) What is the projected deer population in 2016? (Round your answer to the nearest thousand.) deer (d) Estimate how long it takes the population to reach 400,000. (Round your answer to two decimal places.) yr Apr 18 9:45

          The graph shows the deer population in a Pennsylvania county between 2010 and 2014. Assume that the population grows exponentially
(8)4
30,000-
Deer
20,000
population
10,000
0
1 2 3 4
Years since 2010
(a) What was the deer population in 2010?
20,000
deer
(b) Find a function that models the deer population $t$ years after 2010. (Enter your answer in the form $n_0e^{rt}$. Round your $r$ value to four decimal places.)
n(t) =
(c) What is the projected deer population in 2016? (Round your answer to the nearest thousand.)
deer
(d) Estimate how long it takes the population to reach 400,000. (Round your answer to two decimal places.)
yr
Apr 18
9:45
        
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The graph shows the deer population in a Pennsylvania county between 2010 and 2014. Assume that the population grows exponentially
(8)4
30,000-
Deer
20,000
population
10,000
0
1 2 3 4
Years since 2010
(a) What was the deer population in 2010?
20,000
deer
(b) Find a function that models the deer population t years after 2010. (Enter your answer in the form n0e^rt. Round your r value to four decimal places.)
n(t) =
(c) What is the projected deer population in 2016? (Round your answer to the nearest thousand.)
deer
(d) Estimate how long it takes the population to reach 400,000. (Round your answer to two decimal places.)
yr
Apr 18
9:45

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Precalculus with Limits
Ron Larson 2nd Edition
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The grph show the deer populetton In Pennylvona county bwon 210 and 20.Asume thet the populatlon grows exponentilly 30,000 Deer 20,000 population 10,000 0 Years since2010 aWhat was the deer population in 20107 20,000 Vdeer (b)Finda function that models the dee n(t)= c What is the projected deer population in 20167 Round your answer to the nearest thousand deer d Estimate how long it takes the poputation to reach 400.000,Round your answer to two decimal places. lyr
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Deer Population The graph shows the deer population in a Pennsylvania county between 2010 and $2014 .$ Assume that the population grows exponentially. $$ \begin{array}{l}{\text { (a) What was the deer population in } 2010 ?} \\ {\text { (b) Find a function that models the deer population } t \text { years }} \\ {\text { after } 2010 \text { . }} \\ {\text { (c) What is the projected deer population in } 2018 ?}\end{array} $$$$ \begin{array}{l}{\text { (d) Estimate how long it takes the population to reach }} \\ {100,000 .}\end{array} $$

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Transcript

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00:01 Given that the deer population is growing exponentially so we can write n is equal to n0 e to the power rt.
00:08 Now we have been given the graph so from the graph we have to tell what was the deer population in 2010.
00:16 So in 2010 the deer population was simply from graph 20000.
00:23 Now in part b we have to write the function that models the deer population t years after 2010.
00:31 So in 2010 that is n0 initially the population is 20000.
00:37 So now n is equal to 20000 e to the power rt.
00:43 Now we can see that in 2014 that is t is equal to 4 population is 31000.
00:52 So we can use this fact 31000 is equal to 20000 e to the power r into 4.
01:00 So this is 31 by 20 ln 4r.
01:08 So from here we get the value of r as 0 .109...
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