For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r . For interest compounded n times per year, the amount A ( t ) in the account after t years is given by A ( t ) = P ( 1 + r n ) n t . If interest is compounded continuously, the amount is given by A ( t ) = P e r t . Suppose an investor deposits $10,000 in an account earning 6.0% interest compounded continuously. Find the total amount in the account for the following time periods. How does the length of time affect the amount of interest earned? a. 5 yr b. 10 yr c. 15 yr d. 20 yr e. 30 yr
For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r . For interest compounded n times per year, the amount A ( t ) in the account after t years is given by A ( t ) = P ( 1 + r n ) n t . If interest is compounded continuously, the amount is given by A ( t ) = P e r t . Suppose an investor deposits $10,000 in an account earning 6.0% interest compounded continuously. Find the total amount in the account for the following time periods. How does the length of time affect the amount of interest earned? a. 5 yr b. 10 yr c. 15 yr d. 20 yr e. 30 yr
Solution Summary: The author calculates the total amount in an account earning 6% interest compounded continuously for 5 years and the effect time has over the interest.
For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r. For interest compounded n times per year, the amount
A
(
t
)
in the account after t years is given by
A
(
t
)
=
P
(
1
+
r
n
)
n
t
. If interest is compounded continuously, the amount is given by
A
(
t
)
=
P
e
r
t
.
Suppose an investor deposits $10,000 in an account earning 6.0% interest compounded continuously. Find the total amount in the account for the following time periods. How does the length of time affect the amount of interest earned?
At the beginning of the last decade, a total of 7.2 million passengers took a cruise vacation.
The global cruising industry has been growing at approximately 7% per year.
Assume that this growth rate continues.
Suppose N = (t) gives the number of passengers, in millions, that take a cruise vacation at year t.
Answer parts (a), (b), (c), and (d) of the question. Click VERIFY to move to the next part.
(a) Report the following. Use the pull-down menu to indicate the units.
A0) = Number
Click for List
(b) If (t) is written in the form a-b’, do you predict the value of b to be greater than 1 or less than 1?
O b is greater than 1 O b is less than 1
(c) Complete the boxes below to write a formula which gives N as a function of t, where t is in years.
Do not round any values. Since your formula gives N in millions of people,
check that it passes through the initial value x = 0, N= 7.2, as opposed to passing through x = 0, y = 7,200,000.
N=
Number
( Number
(d) How many millions of cruise…
five thousand dollars is deposited into a savings account that has interest compounded continuously. suppose after 3 years the account has grown to six thousand dollars.
A.) find the yearly interest rate r for this savings account
B.) how long will it take for the initial balance to double
2)
An initial investment of $10,000 grows at 11% per year. What function represents the value of the investment after t years?
R) - 10,000(1.11)
R) - 10,000(1.11)
- 10,000(11)'
A) – 10,000(0.11)'
a.
c.
b.
d.
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