Response:
The goat population will reach 1000 in a time span of 12.4 years
Detailed explanation:
After t years, the population of goats is described by
where 
indicates the initial count of goats and b is the growth rate per capita.
Based on the problem,
- b = 0.5
- N = 1000
A(n)=a(1)+(n-1)d=
a(n)=2+(n-1)2=2+2n-2=2n
Answer:
Detailed solution:
Given:
The problem to solve is:
Convert the equation into the standard quadratic form 
, where 
represent constants.
So, by adding 
to both sides, we get:
Note that 
.
The roots of this quadratic are found by applying the quadratic formula given as:
Substitute into the formula and calculate for 
.
Hence, the roots are:
Answer:
2.5 seconds after the initial ball was struck.
Step-by-step explanation:
The height equations are:
At the point where the balls intersect, both heights are alike, therefore:
-16t² + 56t = -16t² + 156t - 248
-16t² + 56t + 16t² - 156t + 248 = 0
- 100t + 248 = 0
248 = 100t
t = 248/100
t = 2.48 ≈ 2.5
