Answer:
24 years
Step-by-step 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
