When billy turns 18 he will have $3,099.6 in his account because .021 percent x $8,200= $172.20 per year x 18 years = $3,099.60
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

Answer:2500
Step-by-step explanation:
no cap
Step-by-step explanation:
I am not sure i understand the text you put there.
what I think is clear is to find the expected number of the appearances of the number 3 when spinning the spinner 100 times.
to do this we start by checking the given information.
and we see that the given table based on the result of in total 50 spins (7+8+9+7+11+8).
when spinning the spinner additional times, we can expect the same structure of distribution of the individual possible results as before. we just scale everything to the new size of the overall sample.
before, with 50 spins, we saw the number 3 9 times.
so, with 100 spins, which is 2×50, we expect to see the number 3 then 2×9 = 18 times.