Question

My last math question of the year, Calculus optimization. Help Please!!

Answer 1

@agent0smith can you help with one last question #12 please

Answer 2

Set the given equations equal to each other

Answer 3

okay

Answer 4

\[Me ^{rt}=Ce ^{k \sqrt{t}}\]

Answer 5

Do I solve for t again?

Answer 6

"how much money M"

Answer 7

so solve for m!

Answer 8

okay do i use the given values from previous problems or just keep all of the variables in it

Answer 9

They don't say. So... variables.

Answer 10

okay

Answer 11

\[M=Ce ^{\sqrt{t}k-tr}\]

Answer 12

Yep

Answer 13

and that is what i am supposed to compare to topt?

Answer 14

Same steps as before, derivative, set to 0 etc

Answer 15

okay

Answer 16

I cant derive this, ive been trying

Answer 17

If you can derive the one from a while ago, you can do this one.

Answer 18

Okay so the derivative of e^f(x) is f'(x)e^f(x)?

Answer 19

Yep, use that

Answer 20

okay

Answer 21

\[Ce ^{k \sqrt{t}-tr}(\frac{ k }{ 2\sqrt{t} }-r)\]

Answer 22

And now set equal to zero and solve for t?

Answer 23

Ill do that

Answer 24

Looks familiar, huh?

Answer 25

yeah it does

Answer 26

is it the same as topt?

Answer 27

@agent0smith

Answer 28

Yeah when I said it looks familiar, i meant cos it looks exactly the same!

Answer 29

yeah haha thanks mate!

Answer 30

Welcome mate!

Answer 31

I hope you have a great summer and Thanks for all of the help sir!! God Bless!!

Answer 32

You too!