Your aunt matilda passes away and leaves you with the tidy sum of $50,000. you find a bank that will pay you 5.15 % per year compounded every instant. you want to enjoy some of this money, but you don't want to blow it away too fast. you decide to deposit the $50,000 but to pull out d dollars per year so that after t years, you will have blown (d t) dollars off. if p [t] is the amount in the account, then why does p [t] solve the differential equation p'[t] - 0.0515 p[t] = -d ?

Deduction in the step-by-step explanation

Step-by-step explanation:

If a P0=50.000 deposit is compound every instant, the ammount in the account can be modeled as:

If you pull out d dollars a year, the equation becomes:

If we derive this equation in terms of t, we have

The first term can be transformed like this:

So replacing in the differential equation, we have

Rearranging

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

yes

step-by-step explanation: