Question

Calculus optimization problem help please fan and medal!!

Answer 1

I need help with #4 please

Answer 2

Here are some screenshots because some people don't like opening pdf files

Answer 3

@agent0smith

Answer 4

The initial investment will be given by the V(t) formula. \[\Large I_0 = C e^{k \sqrt t}\]since that is the value of the card when he sells it and thus invests the money.

Then just plug that into the formula for the given investment formula.

Answer 5

so i subsitute t for 65 years?

Answer 6

No. You don't know when he sells the card, just that it's t years after t=0.

t is how long he held onto the card. Which means the time in the investment formula A(t) has to be 40-t... since, for example, if he keeps the card for 10 years then sells it, then he'd have invested the money in his account for the other 30 years (till he's 65)

\[\Large A(t) = I_0 e^{r(40-t)}\]then just plug in the Io expression from above.

Answer 7

so it would be
\[A(t)=(Ce ^{k \sqrt{t}})e ^{r(40-t)}\]

Answer 8

Right. The most confusing part was figuring out the time in the equations, with the way the question is worded. But since the t for holding/selling the card is anywhere from 0 to 40, the time for investing must be 40-t.

Answer 9

Okay that makes sense thanks mate!!

Answer 10

Welcome.

Answer 11

Wow, brain goals. Good job, danno!

Answer 12

haha good job indeed

Answer 13

This is what the graph would look like for c = 2500, k=0.5, and r=0.06?

Answer 14

Keep in mind 0<t<40...he's not gonna live 200 years.

Answer 15

so the graph only counts after y = 2500?

Answer 16

Well probably, but i'm saying restrict the domain.

You can and maybe should also simplify using exponent rules, adding the e exponents:
\[\Large A(t)=(Ce ^{k \sqrt{t}})e ^{r(40-t)} = C e^{k \sqrt t+ r(40-t)}\]

Answer 17

Okay i will try to graph that one then

Answer 18

\[\Large A(t)= 2500 e^{0.5 \sqrt t+ 0.06(40-t)}\] but make sure to restrict the domain.

Answer 19

okay

Answer 20

i would restrict it to 65 because it is 65 years?

Answer 21

or what do i restrict it to

Answer 22

The question literally tells you the t domain. And i gave the same thing a few posts back.

Answer 23

Yeha my bad i saw that after i posted the question

Answer 24

i feel stupid now

Answer 25

http://www.wolframalpha.com/input/?i=A(t)%3D+2500+e%5E%7B0.5+%5Csqrt+t%2B+0.06(40-t)%7D+for+t%3D0+to+t%3D40

Answer 26

thanks mate!!