Chapter 12 Sequences; Induction; the Binomial Theorem

Chapter 12: Sequences; Induction; the Binomial Theorem
c. Scrolling down the table, we find that
balance is paid off in the 39th month. The
last payment is $54.18. There are 38
payments of $534.47 and the last payment
of $54.18 plus interest. The total amount
paid is: 38(534.47) + 54.18(1.005) =
$20,364.31.
d. The interest expense is:
20,364.31 – 18,500.00 = $1864.31
85. a. p1
= 1.03(2000) + 20 = 2080;
p2
= 1.03(2080) + 20 = 2162.4
There are approximately 2162 trout in the
pond at the end of the second month.
b. Scrolling down the table, we find the trout
population exceeds 5000 at the end of the
26th month when the population is 5084.
c. The equilibrium level of pollution occurs
when x = 0.9x+ 15 . That is, when x = 150
tons.
x = 0.9x+
15
0.1x
= 15
x = 150
87. a. Since the fund returns 8% compound
annually, this is equivalent to a return of 2%
each quarter. Defining a recursive
sequence, we have:
a0 = 0, an
= 1.02an
− 1+
500
b. Insert the formulas in your graphing utility
and use the table feature to find when the
value of the account will exceed $100,000:
86. a. p1
= 0.9(250) + 15 = 240;
p2
= 0.9(240) + 15 = 231
There are 240 tons of pollutants at the end of
the first year, and 231 tons of pollutants at
the end of the second year.
b. Scrolling down the table, we display the
pollutant levels for the next 20 years.
In the 82nd quarter (approximately May
2019) the value of the account will exceed
$100,000 with a value of $101,810.
1240
© 2009 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.