1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
algol13
3 years ago
9

If $1000 is invested at 8% interest, compounded annually, then after n years the investment is worthan = 1000(1.08)ndollars.(a)

Find the first five terms of the sequence {an}. (Round your answers to the nearest cent.)a1 = $a2 = $a3 = $a4 = $a5 = $(b) Is the sequence convergent or divergent?
Mathematics
1 answer:
Luba_88 [7]3 years ago
5 0

Answer:

Diverge

Step-by-step explanation:

(a)

1st year: 1000 * 1.08^1 = \$1080

2nd year: 1000 * 1.08^2 = \$1166.4

3rd year: 1000 * 1.08^3 = \$1259.71

4th year: 1000 * 1.08^4 = \$1360.49

5th year: 1000 * 1.08^5 = \$1469.33

(b) The sequence is divergent, because if we take the derivative of the function with respect to n year:

(1000*1.08^n)^{'} = 1000ln(n)*1.08^n

This is a positive, meaning the slope of the function is positive. If we take the second derivative using product rule

(1000ln(n)*1.08^n)^{'} = 1000\frac{ln(n)}{n}1.08^n

This is also positive when n > 0. Therefore, the slope is positive and increasing. This means the sequence diverges.

You might be interested in
Which is the graph of g(x) = [X +3]?
Daniel [21]

Answer:

b

Step-by-step explanation:

just took it i got 100%

4 0
3 years ago
Graph the function f(x) = x3 – 4x – 1. Which are approximate solutions for x when f(x) = 0?
Scilla [17]
If f(x) is = to 0 then that means that you would have to plug the 0 in for all of the x that are in the function and the solve it.
f(x)= x3-4x-1
f(0)= (0)3-4(0)-1
0        0        0 -1
-1 
so that means that -1 would be the answer for the function
5 0
3 years ago
Read 2 more answers
Find the distance between (2, 2) and (-4, 4). Round answer to the nearest tenth.
Naya [18.7K]

Answer:

6.3

Step-by-step explanation:

First off, we need the distance formula, which is:

\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

If we plug in the points, we get:

\sqrt{(-4 - 2)^2 + (4 - 2)^2}

If we simplify everything under the square root, we get:

\sqrt{(-6)^2 + (2)^2}

\sqrt{36 + 4}

\sqrt{40}

In decimal, the answer is 6.3

6 0
3 years ago
Dustin collects football cards.
Setler79 [48]
<em>Total Price = 3+5+5+8+8+10+10+10+40 = 99

</em>
\frac{99}{9} =11<em>
</em>
6 0
3 years ago
Juniper wants to make a new rectangular garden in her backyard that has a length that is 2 more than twice the width. She needs
lisabon 2012 [21]

Answer:

2x+2y ≤ 64

x=2y+2

Step-by-step explanation:

x = length

y = width

the length is 2 more than twice the width or 2 more than twice y

x = 2+2y

the perimeter of the garden = 2 times the length + 2 times the width

she have 64ft of wire so the perimeter should be equal or less than 64 ft

64 ≥ 2x + 2y

5 0
3 years ago
Other questions:
  • : Resolver el sistema de ecuaciones por el método de reducción. -x + 3y = 6 x + y = 2
    5·1 answer
  • Write the expression <br> 6 less 7 times a number
    10·2 answers
  • (Express each rate in lowest term)<br>6 + 4 2/3​
    12·1 answer
  • What is 0.03 in scientific notation
    5·1 answer
  • What is the 100th term in the list?<br>10<br>17<br>24<br>31<br>38​
    9·1 answer
  • Which two FRACTIONS below have a DIFFERENCE of 27/40?
    11·2 answers
  • A rectangle has an area of 22.64 inches squared. If the coordinates of one of its sides are (0, 0) and (4, 4), what are the dime
    14·1 answer
  • 21, 18, 45, 33, 4, 12, 21<br><br> Mean:<br><br> Median:<br><br> Mode:<br><br> Range:
    12·1 answer
  • The average distance from Earth to the Sun is 92.95 million miles. The actual distance varies from the average by up to 1.55 mil
    11·1 answer
  • (1+sinx/cosx)+(cosx/1+sin)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!