Find the function rule for g(x). The function f(x) = x2 . The graph of g(x) is f(x) translated to the right 8 units and down 7 u
1 answer:
You might be interested in
Answer:
a.
b. 1.5
c. 1.5
d. No
Step-by-step explanation:
a. First, let's solve the differential equation:
Divide both sides by and multiply both sides by dt:
Integrate both sides:
Evaluate the integrals and simplify:
Where C1 is an arbitrary constant
I sketched the direction field using a computer software. You can see it in the picture that I attached you.
b. First let's find the constant C1 for the initial condition given:
Solving for C1:
Now, let's evaluate the limit:
The expression tends to zero as x approaches ∞ . Hence:
c. As we did before, let's find the constant C1 for the initial condition given:
Solving for C1:
Now, let's evaluate the limit:
The expression tends to zero as x approaches ∞ . Hence:
d. To figure out that, we need to do the same procedure as we did before. So, let's find the constant C1 for the initial condition given:
Solving for C1:
Can a population of 2000 ever decline to 800? well, let's find the limit of the function when it approaches to ∞:
The expression tends to zero as x approaches ∞ . Hence:
Therefore, a population of 2000 never will decline to 800.
