Question

M'(t)=90t-3t^2 new cases every day. If there were 30 cases reported on the first day, how many new cases were reported on the 7th day?

Answer 1

M'(t) is the derivative of the number of cases reported?

Answer 2

yes

Answer 3

OK, great!
So, to find M(t) we hav eto integrate M'(t)
\[M(t)=\int\limits_{}^{}90t-3t^2 dt\]
Do you know how to integrate that?

Answer 4

thats where Im having my trouble is integrating this problem

Answer 5

M(t)=45t^2-t^3 +constant
To find the constant we have to use this:
M(1)=30 (" If there were 30 cases reported on the first day")
Can you continue now?

Answer 6

what variable do i put 30 in

Answer 7

You have to plug 30 instead of M(t) and 1 instead of t.

Answer 8

so you plug 30 to find C

Answer 9

\[30=45*(1)^2-1+C\]
Solve for C.

Answer 10

did you get -14 for C
@rafabc02

Answer 11

Perfect! Well done!

Answer 12

how many new cases were reported on the 7th day?

Answer 13

so then do you plug -14 into
45t^2-t^3+C

Answer 14

C=-14
So:
\[M(t)=45t^2-t^3 -14\]

Answer 15

so you put 7 into t?

Answer 16

That's it!
What do you get?

Answer 17

1848

Answer 18

You got it! Congratulations!
Any doubt about any step?
(Thanks for "best response"!)
:)

Answer 19

nope I think I am ok! Thanks!

Answer 20

Thanks to you! ;)