Question

Intro to rates of change...How do I do this FIRST question? lol :( (see attatched)

Answer 1

We only learned power rule

Answer 2

rate of change is:
\[\frac{ \Delta b }{ \Delta t } = \frac{ db }{ dt }\]
where b = change in number of bacteria

Answer 3

oh we didnt learn that dbthing yet

Answer 4

wait thats ust slope?

Answer 5

*jsut

Answer 6

\[\frac{ db }{ dt }\] is the derivative, which can be thought of as how much one quantity is changing in response to changes in some other quantity. in this case, it is the change in bacteria amount over time.
\[\frac{ \Delta b }{ \Delta t }\] is the same thing, just different notation.
\[\Delta = change\]
the triangle greek symbol means change.
The derivative also represents the slope as you mentioned. It is the tangent line to a particular function, which takes the form:
\[\frac{ \Delta y }{ \Delta x } = \frac{ y_2 - y_1 }{ x_2 - x_1 } = m = slope\]

Answer 7

I thought this was for a calculus course which is why I mentioned derivatives, but you can ignore the db/dt stuff. You mentioned power rule and I thought of something else. My bad. I didn't mean to confuse you.

Answer 8

Ohh ok thank you

Answer 9

Thanks for your help!

Answer 10

No problem. Good luck.