By solving a quadratic equation, it can be verified that
The owl population will disappear after 329.12 years
What is a quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as quadratic equation.
Here, a quadratic equation needs to be solved
The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p=![-0. 4t^2+128t+1,200](https://tex.z-dn.net/?f=-0.%204t%5E2%2B128t%2B1%2C200)
For population to disappear, p =0
![-0. 4t^2+128t+1,200 = 0\\0.4t^2 -128t - 1200 = 0\\4t^2 - 1280t - 12000 = 0\\4(t^2 - 320 t - 3000) = 0\\t^2 - 320t -3000 = 0\\t = \frac{-(-320)\pm \sqrt{(-320)^2 - 4 \times 1 \times (-3000)}}{2 \times 1}\\t = \frac{320 \pm 338.23}{2}\\t = \frac{320 + 338.23}{2} \ or \ t = \frac{320 - 338.23}{2}\\t = 329.115 \ or \ t = -9.115](https://tex.z-dn.net/?f=-0.%204t%5E2%2B128t%2B1%2C200%20%3D%200%5C%5C0.4t%5E2%20-128t%20-%201200%20%3D%200%5C%5C4t%5E2%20-%201280t%20-%2012000%20%3D%200%5C%5C4%28t%5E2%20-%20320%20t%20-%203000%29%20%3D%200%5C%5Ct%5E2%20-%20320t%20-3000%20%3D%200%5C%5Ct%20%3D%20%5Cfrac%7B-%28-320%29%5Cpm%20%5Csqrt%7B%28-320%29%5E2%20-%204%20%5Ctimes%201%20%5Ctimes%20%28-3000%29%7D%7D%7B2%20%5Ctimes%201%7D%5C%5Ct%20%3D%20%5Cfrac%7B320%20%5Cpm%20338.23%7D%7B2%7D%5C%5Ct%20%3D%20%5Cfrac%7B320%20%2B%20338.23%7D%7B2%7D%20%5C%20or%20%5C%20t%20%3D%20%5Cfrac%7B320%20-%20338.23%7D%7B2%7D%5C%5Ct%20%3D%20329.115%20%5C%20or%20%5C%20t%20%3D%20-9.115)
But t = -9.115 is not possible as time cannot be negative
So, the owl population will disappear after 329.12 years
To learn more about quadratic equation, refer to the link-
brainly.com/question/1214333
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