You are here:

Algebra/Recursive Sequence

Advertisement


Question
You complain that your hotel room is too cold. The hotel tells you that they will increase the temperature by 8% each hour. If the current temperature of the room is 72 degrees F, what will the temperature be after 4 hours, to the nearest tenth of a degree?

Is this sequence geometric or arithmetic?

Write a recursive formula for the sequence.

Answer
Let t(n) be the temperature in the room after n hours.

The room starts at 72 , so

t(0) = 72

After 1 hour, the temperature increases by 8%

t(1) = (1.08)(72) = 77.76

After 2 hours , the temperature increases by 8% again

t(2) = (1.08)(77.76) = 83.98

continue in this way , multiplying by 1.08 two more times

t(3) = (1.08)(83.98) = 90.7

t(4) = (1.08)(90.7) = 97.95


After 4 hours , the temperature will be 98 degrees , to the nearest tenth.

Since we keep finding the next temperature in the sequence by multiplying by 1.08 , the sequence is geometric.

A recursive formula for the sequence is t(n+1) = (1.08)t(n)  , n = 0,1,2....,  with t(0) = 72

This gives t(n) = (72)(1.08)^n  

Algebra

All Answers


Answers by Expert:


Ask Experts

Volunteer


Socrates

Expertise

Any questions on High School Algebra, College Algebra, Abstract Algebra. I can help with word problems, solving equations, trigonometry, inequalities, Gaussian Elimination, Linear Algebra, groups, fields, you name it!

Experience

Ph.D. in Mathematics, specialist in Algebra. I have taught High School students and college students at three state universities.

Organizations
Mathematical Association of America. American Mathematical Society.

Publications
Regular contributions to the problems section of the American Mathematical Monthly journal.

Education/Credentials
B.S., M.S., Ph.D.

©2016 About.com. All rights reserved.