Question

Quick help with calculus question.

Answer 1

I have no examples in any of my 6 homework assignments. Pearson likes to add questions onto quizzes or tests that I dont know how to solve since they are not on the homework assignments.

Answer 2

I assume I would just plug 1800 where t is.

Answer 3

\(\ln 6 = - \dfrac{t}{100}\)

Answer 4

Could you explain where you got all of that from?

Answer 5

Let's set it up like algebra

Since you want to find when the population will equal 1800, let's set the equation equal to 1800

\[1800= 300 e^{ .01t}\]

We want to first get the 300 to the other side of the equation

Answer 6

Okay. So divide 300 to the other side.

Answer 7

Next simplify 1800/300 and then put Ln in front of it and the e?

Answer 8

Yes

Answer 9

That gets rid of the e

Answer 10

1800 divided by 300= 6 so should I just put that? This is the first time it hasn't been a fraction.

Answer 11

So the answer is 179.2?

Answer 12

So after dividing we got

\[6 = e^{.01t}\]

We said to get rid of the E, we use natural log, so:

\[\ln(6) = \ln e^{.01t}\]

That gets rid of the e, so:

\[\ln(6) = .01t\]

And yes, it does

Answer 13

Okay. Can you help me with one more?

Answer 14

Differentiate.
y= Lnx over x^7

Answer 15

\[\frac{ d }{ dx }\frac{ \ln(x) }{ x^7 }\]

Let's try the quotient rule

Answer 16

Okay.

Answer 17

\[f(x) = \ln(x) \]
\[g(x) = x^7\]

So it would be

\[\frac{ g(x)*f'(x)-f(x)*g'(x) }{ g(x)^2 }\]

Answer 18

in short, you need to solve for "t"
and since "t" is an exponent, the way to get it "down", is to apply logs

Answer 19

So the answer is 1 over x^8 - 7Ln(x) over x^8 ?

Answer 20

@jdoe0001 what?

Answer 21

\[\frac{ \frac{ 1 }{ x^8 }-7\ln(x) }{ x^8 }\]

Is that what you meant?

Answer 22

Nope.
1/x^8 - 7Ln(x) /x^8

two separate fractions

Answer 23

Or should it be
1- 7Ln(x) over x^8

Answer 24

Sorry, Im trying to convert it. Is it this:

\[\frac{ 1 }{ x^8 }-\frac{ 7\ln(x) }{ x^8 }\]

Answer 25

\[\frac{ 1-7\ln(x) }{ x^8 }\] sounds good too

Answer 26

Okay. So either would be fine?

Answer 27

Yeah, I don't know which one the system would accept though

Answer 28

hmmmm

Answer 29

Im going with only one fraction. If Pearson marks me wrong then ill send an email to my professor about it. Then he will give me the point.

Answer 30

Thank you for helping!

Answer 31

You're welcome =)