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
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ISBN:9780079039897
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Chapter7: Exponents And Exponential Functions
Section7.9: Geometric Sequences As Exponential Functions
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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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