Explanation Given information: A rich man gives $ 1000 on September 1 , and thereafter he will give 9 10 of what he gave the previous day. Formula used: Let { a n } be a geometric sequence with first term a 1 and common ratio r , where r ≠ 0 , 1 . The sum S n of the first n terms of { a n } is S n = a 1 + a 1 r + a 1 r 2 + ⋅ ⋅ ⋅ + a 1 r n − 1 = ∑ k = 1 n a 1 r k − 1 = a 1 ⋅ 1 − r n 1 − r Calculation: Assume the received amount is less than 1 cent after n number of days from September 1 The amount received after n number of days can be calculated by a n = a r n − 1 Here, a = 1000 and r = 9 10 = 0.9 ⇒ 1000 ( 0.9 ) n − 1 < 0.01 ⇒ ( 0.9 ) n − 1 < 0.01 1000 ⇒ ( 0

11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 12.3, Problem 101AYU

To determine

To calculate: The first date on which the received amount is less than 1 cent and the total amount received up to that day, if a rich man gives $1000 on September 1, and thereafter he will give 910 of what he gave the previous day.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 100AYU

Chapter 12.3, Problem 102AYU

Students have asked these similar questions

Determine whether the series is convergent or divergent. Justify your answer. If the series is convergent, you do not have to find its sum. n=0 (-1) 72n+1 (2n)!

+ Find the first five non-zero terms of the Taylor series for f(x) = sin(2x) centered at 4π. + + + ...

+ + ... Find the first five non-zero terms of the Taylor series for f(x) centered at x = 4. = 1 x + + +

Chapter 12 Solutions

Precalculus

Ch. 12.1 - For the function f( x )= x1 x , find f( 2 ) and f(...Ch. 12.1 - True or False A function is a relation between two...Ch. 12.1 - Prob. 3AYU Ch. 12.1 - True or False The notation a 5 represents the...Ch. 12.1 - True or False If is am integer, then Ch. 12.1 - The sequence a 1 =5 , a n =3 a n1 is an example of...Ch. 12.1 - The notation a 1 + a 2 + a 3 ++ a n = k=1 n a k...Ch. 12.1 - k=1 n k=1+2+3++n = ______. (a) n! (b) n( n+1 ) 2...Ch. 12.1 - In Problems 11-16, evaluate each factorial...Ch. 12.1 - Prob. 10AYU

Additional Math Textbook Solutions

Find more solutions based on key concepts

In Exercises 11-20, express each decimal as a percent. 11. 0.59

Thinking Mathematically (6th Edition)

Whether the requirements for a hypothesis test are satisfied or not.

Elementary Statistics

Two cards are randomly selected from an ordinary playing deck. What is the probability that they loin, a blackj...

A First Course in Probability (10th Edition)

The equivalent expression of x(y+z) by using the commutative property.

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Trigonometric substitutions Evaluate the following integrals. 31. x29xdx,x3

Calculus: Early Transcendentals (2nd Edition)

Time Employed A human resources manager for a large company takes a random sample of 50 employees from the comp...

Introductory Statistics

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The first date on which the received amount is less than 1 cent and the total amount received up to that day, if a rich man gives $ 1000 on September 1 , and thereafter he will give 9 10 of what he gave the previous day.

Solution Summary: The author calculates the amount received after n number of days.