A fishery stocks a pond with 1000 young trout.  The number of trout t years later is given by Q(t) = 1000e(−0.5t).  Graph the number of trout against time.  Do this on extra paper.How many trout are left after 1 year ____________________________?Find Q(3) and interpret your answer in terms of trout _____________________?At what time are there 100 trout left _________________________________?  a.A. Approximately 606 Trout;  B. Approximately 223 and means that after 3 years      the pond will have about 223 trout left.  C.  Approximately 4.6 years b.A. Approximately 606 Trout;  B. Approximately 223 and means that after 3 years      the pond will have about 223 trout left.  C.  Approximately 1.6 years c.A. Approximately 606 Trout;  B. Approximately 2231 and means that after 3 years      the pond will have about 223 trout left.  C.  Approximately 4.6 years d.A. Approximately 900 Trout;  B. Approximately 223 and means that after 3 years      the pond will have about 223 trout left.  C.  Approximately 1.6 years e.None of these

Question
Asked Sep 13, 2019
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A fishery stocks a pond with 1000 young trout.  The number of trout t years later is given by Q(t) = 1000e(−0.5t).  Graph the number of trout against time.  Do this on extra paper.

  1. How many trout are left after 1 year ____________________________?
  2. Find Q(3) and interpret your answer in terms of trout _____________________?
  3. At what time are there 100 trout left _________________________________?

 

  a.

A. Approximately 606 Trout;  B. Approximately 223 and means that after 3 years
      the pond will have about 223 trout left.  C.  Approximately 4.6 years

  b.

A. Approximately 606 Trout;  B. Approximately 223 and means that after 3 years
      the pond will have about 223 trout left.  C.  Approximately 1.6 years

  c.

A. Approximately 606 Trout;  B. Approximately 2231 and means that after 3 years
      the pond will have about 223 trout left.  C.  Approximately 4.6 years

  d.

A. Approximately 900 Trout;  B. Approximately 223 and means that after 3 years
      the pond will have about 223 trout left.  C.  Approximately 1.6 years

  e.

None of these

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Expert Answer

Step 1

(a)

Find the number of trout are left after 1 year.

The number trout t years later given by O(t)= 1000e)
Substitute 1 for t in Q(t)=1000e0.51)
(1) 1000e01)
=1000e05)
1000
1000
1.64872
606
Thus, the number of trout are left after 1 year is 606 approximately
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Image Transcriptionclose

The number trout t years later given by O(t)= 1000e) Substitute 1 for t in Q(t)=1000e0.51) (1) 1000e01) =1000e05) 1000 1000 1.64872 606 Thus, the number of trout are left after 1 year is 606 approximately

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Step 2

(b)

Find the number of trout are left after 3 years.

The number trout t years later given by O(t)= 1000e)
Substitute 3 for t in Q(t)=1000e0.51)
g(3) =1000e-05(3)
=1000e-15)
1000
1000
4.48168
223
Thus, the number of trout are left after 3 year is 223 approximately
help_outline

Image Transcriptionclose

The number trout t years later given by O(t)= 1000e) Substitute 3 for t in Q(t)=1000e0.51) g(3) =1000e-05(3) =1000e-15) 1000 1000 4.48168 223 Thus, the number of trout are left after 3 year is 223 approximately

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Step 3

(c)

Find the time when there a...

The number trout t years later given by O(t)= 1000e051)
Substitute 100 for Q(t)in Q(t)=1000e
100 1000e0.5t)
100
1000et)
1000
1000
1
(-0.5t
10
In(e-25)
(-0.5r)
= In
10
1
-0.5t n
10
1
In
10
t
-0.5
4.6 years
Thus, the time when there are 100 trout left is 4.6years
Hence the required
answer is Option (a)
help_outline

Image Transcriptionclose

The number trout t years later given by O(t)= 1000e051) Substitute 100 for Q(t)in Q(t)=1000e 100 1000e0.5t) 100 1000et) 1000 1000 1 (-0.5t 10 In(e-25) (-0.5r) = In 10 1 -0.5t n 10 1 In 10 t -0.5 4.6 years Thus, the time when there are 100 trout left is 4.6years Hence the required answer is Option (a)

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Math

Calculus

Functions