Trout Population A pond currently contains 2000 trout. A fish hatchery decides to add 20 trout each month. It is also known that the trout population is growing at a rate of 3 % per month. The size of the population after n months is given by the recursively defined sequence p 0 = $ 3000 p n = 1.03 p n − 1 + 20 . How many trout are in the pond after 2 months? That is. what is p 2 ?
Trout Population A pond currently contains 2000 trout. A fish hatchery decides to add 20 trout each month. It is also known that the trout population is growing at a rate of 3 % per month. The size of the population after n months is given by the recursively defined sequence p 0 = $ 3000 p n = 1.03 p n − 1 + 20 . How many trout are in the pond after 2 months? That is. what is p 2 ?
Solution Summary: The author calculates the number of trout in the pond after 2 months, that is P_2=2162.
Trout Population A pond currently contains
2000
trout. A fish hatchery decides to add
20
trout each month. It is also known that the trout population is growing at a rate of
3
%
per month. The size of the population after
n
months is given by the recursively defined sequence
p
0
=
$
3000
p
n
=
1.03
p
n
−
1
+
20
.
How many trout are in the pond after
2
months? That is. what is
p
2
?
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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