Question

The number y of deer in a county after x years can be modeled by y=0.75x^2 + 10.5x + 1300. When were there about 2000 deer? Round your answer to the nearest whole number.

Answer 1

24 years

Explanation:

We are told that the model of number of deers is;

y = 0.75x² + 10.5x + 1300

Where;

y represents number of deers

x represents number of years

Now, we want to find how many years it will take to get to 2000 deers.

Thus;

2000 = 0.75x² + 10.5x + 1300

0.75x² + 10.5x + 1300 - 2000 = 0

0.75x² + 10.5x - 700 = 0

Using quadratic formula, we have;

x = [-b ± √(b² - 4ac)]/2a

x = [-10.5 ± √(10.5²- (4*0.75*-700)]/(2*0.75)

x = [-10.5 ± √(110.25 + 2100)]/(1.5)

x = [-10.5 ± √2210.25]/(1.5)

x ≈ -38 or 24

Number of years can't be negative, so we will take the positive value.

So, x = 24 years