Answer:
"Multiply the previous value by 2"
Step-by-step explanation:
Let's check the first 2 terms for all the answer choices.
1. Add to the previous value:
Doesn't match.
2. Subtract from the previous value:
Doesn't match.
3. Divide the previous value by 2:
Doesn't match.
4. Multiply the previous value by 2:
DOES WORK!
Also, doing the same thing with all the other values would give us matching answer. So this choice is right.
It looks like the ODE is
with the initial condition of .
Rewrite the right side in terms of the unit step function,
In this case, we have
The Laplace transform of the step function is easy to compute:
So, taking the Laplace transform of both sides of the ODE, we get
Solve for :
We can split the first term into partial fractions:
If , then
.
If , then
.
Take the inverse transform of both sides, recalling that
where is the Laplace transform of the function
. We have
We then end up with