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Algebra
Pregunta

2. In a certain region of the Indian Ocean, the po...

2. In a certain region of the Indian Ocean, the population of Dolphins was \( 81 \) in \( 2003 . \) In \( 2016 \) , the population was \( 70 \) . Assume that the population is modeled by a linear function. a) ( \( 4 \) pts) Find an equation that models the population, \( p ( t ) \) , of Dolphins at any time \( t \) years after \( 2003 \) . b) (1 pts) Use your equation to predict the population of Dolphins in the year \( 2027 \) . Round to the nearest whole number. c) ( \( 3 \) pts) Use your equation to predict in what year the population reaches \( 0 \) . Round your answer to the nearest whole number. 

Answer

a)

if we take 2003 as t = 0, then,

 

slope = (70 - 81) / (13 - 0) = -11/13

y-intercept = p(0) = 81

 

So, the equation of the line is, p(t) = -(11/13)t + 81 

 

b)

if the year is 2027, then t = 2027 - 2003 = 24

 

So, p(24) = -(11/13)24 + 81 = 61

 

c)

That is p(t) = 0,

 

So,

-(11/13)t + 81 = 0

(11/13)t = 81

t = (13/11)×81 = 96 years after 2003.

 

That is in the year = 2003 + 96 = 2099.

Solución
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