Question

The population P, of Caribou in the Yukon is modeled by P=6x^2-120x+1250 where X is the number of years from today. After how many years with the Caribou population route 21,000 round to one decimal place

Answer 1

It will take approximately 68.2 years for the Caribou population to reach 21,000.

Explanation:

The population P of Caribou in the Yukon is modeled by P=6x²-120x+1250 where x is the number of years from today.

If the population P of Caribou in the Yukon is 21000, then, replacing you get:

21000= 6x²-120x+1250

So:

0= 6x²-120x+1250 -21000

0= 6x²-120x - 19750

This is a quadratic function of the form: 0= ax²+ bx +c, where: a=6, b= -120 and c=-19750

To solve a quadratic function and determine the value of x you can use the expression:

`x1,x2=\frac{-b+-\sqrt{b^(2)-4*a*c } }{2*a}`

Replacing the values ​​of a, b and c and solving you get:

`x1,x2=\frac{-(-120)+-\sqrt{(-120)^(2)-4*6*(-19750) } }{2*6}`

`x1,x2=(120+-√(14400+474000 ) )/(12)`

`x1,x2=(120+-√(488400 ) )/(12)`

`x1,x2=(120+-698.86 )/(12)`

So:

`x1=(120+698.86 )/(12)`

x1= 68.24 ≅ 68.2

and

`x2=(120-698.86 )/(12)`

x2= -48. 24 ≅ -48.2

As time cannot be negative, it will take approximately 68.2 years for the Caribou population to reach 21,000.