Question

P(t) = 6e^0.2t/(4+2e^0.2t) determine average rate of change of the population for 0<=t<=20
Find a time at which instantaneous rate of change of population is equal to the average rate of change

Answer 1

@Mertsj

Answer 2

@dumbcow

Answer 3

Firstly find f(0) and f(20)
Then we need to find the average rate of change from 0<t<20
So we would use the following formula
\[\text {Average Rate of Change } =\frac{f(20)-f(0)}{20-0}\]

Answer 4

Ok yes and I got like .0947

Answer 5

set that equal to P'(t) ..... solve for t

Answer 6

use quotient rule for finding derivative

Answer 7

You can always relate rate of change to derivative(side note). It essentially implies take the derivative :)

Answer 8

So check is this right 1.2e^.2t/(4+2e^.2)^2

Answer 9

Opps Should be 1.2e^.2t/(4+2e^.2t)^2

Answer 10

Is that right ?

Answer 11

pretty close ... a 2 can be factored out of denominator

Answer 12

1.2e^.2t/(2+e^.2t)^2

Answer 13

So now how do I solve when set equal to .0947 ? Cross multiply ?

Answer 14

yeah, looks like you will need to distribute it out and get a quadratic

Answer 15

So i get 0.3788e^.2t+.0947e^.4t+0.3788=1.2e^.2t

Answer 16

@FibonacciChick666

Answer 17

hm?

Answer 18

How do now solve this

Answer 19

for instantaneous? get the derivative and evaluate the difference between 0 and 20

Answer 20

sorry misread, no just do what dumbcow did

Answer 21

But thats where I went but how do I solve from there ?

Answer 22

combine the .2 terms to get a quadratic then use e^.4t=x^2

Answer 23

That I think is what I'd do

Answer 24

Ah :)

Answer 25

?? I am getting imaginary numbers

Answer 26

I did ln and got a number thanks

Answer 27

@iambatman

Answer 28

@Spectrum

Answer 29

@sourwing

Answer 30

Please help I just want to finish this one

Answer 31

other people already told you how to do it. Just find the slope

Answer 32

So I found derivitave an set it equal to the 0.0947 how now do I solve for t

Answer 33

??

Answer 34

@Directrix

Answer 35

How do I solve this help!

Answer 36

:(