An investment grows exponentially under continuous compounding. After 2 yr , the amount in thee account is $ 7328.70. After 5 yr, the amount in the account is $ 8774.10. Use the model A t = P e r t to a. Find the interest rate r . Round to the nearest percent. b. Find the original principal P . Round the nearest dollar. c. Determine the amount of time required for the account to reach a value of $ 15 , 000. Round to the nearest year.
An investment grows exponentially under continuous compounding. After 2 yr , the amount in thee account is $ 7328.70. After 5 yr, the amount in the account is $ 8774.10. Use the model A t = P e r t to a. Find the interest rate r . Round to the nearest percent. b. Find the original principal P . Round the nearest dollar. c. Determine the amount of time required for the account to reach a value of $ 15 , 000. Round to the nearest year.
Solution Summary: The author calculates the interest rate r and round off to the nearest percent using the model A(t)=Pekt.
An investment grows exponentially under continuous compounding. After
2
yr
, the amount in thee account is
$
7328.70.
After
5
yr,
the amount in the account is
$
8774.10.
Use the model
A
t
=
P
e
r
t
to
a. Find the interest rate
r
.
Round to the nearest percent.
b. Find the original principal
P
.
Round the nearest dollar.
c. Determine the amount of time required for the account to reach a value of
$
15
,
000.
Round to the nearest year.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
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?
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