In 2010 , the population of a colony is 12000 , and is decreasing exponentially at a rate of 2.1% per year. (a) What will the population be in the year 2034 ? (b) In what year will half of the population be left?
In 2010 , the population of a colony is 12000 , and is decreasing exponentially at a rate of 2.1% per year. (a) What will the population be in the year 2034 ? (b) In what year will half of the population be left?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.9: Geometric Sequences As Exponential Functions
Problem 49PFA
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In 2010 , the population of a colony is 12000 , and is decreasing exponentially at a rate of 2.1% per year.
(a) What will the population be in the year 2034 ?
(b) In what year will half of the population be left?
Expert Solution
Step 1
(a) It is given that, in 2010 the population of a colony is 12000, that is, the initial amount is P = 12000 and the rate is 2.1% per year, that is, r = 0.021.
Let t = 0 represents the year 2010, then t = 24 represents the year 2034.
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