Question

the population of elephants, N, in a national park is modelled.
a)the minimum number of elephants predicts

please help!

Answer 1

\[N=100+4t+400e ^{\frac{ -t }{ 10 }}\]

Answer 2

find the derivative :
N' = 4 + 400 * (-1/10) * e(-t/10) = 0 at critical points

solve this for t and substitute this value in the formula for N

Answer 3

t=-loge(1/10) but the second question is asking em when this minimum occur when the park opened since 1 jan 1986 :( i am lost..

Answer 4

i get -10 ln (1/10)

i'll re check

Answer 5

yeh whats what i got as well
but how could it be the minimum number of elephants predicted? and how do i know when this minimumm will occur?

Answer 6

-t/10 is the exponent right?

Answer 7

- 10 ln(1/10) is the time in years when the minimum is predicted
what does the question as k for exactly?

Answer 8

that value ( time)is 23 .026 years

Answer 9

what do you mean by k? there is no k on equation or on question..

Answer 10

lol - thats meant to be ask

Answer 11

ah.. lol wait if it is asking me the minimum number of elephants predicted. shouldnt i sub in 0 into x?

Answer 12

no you should plug in t = -10 loge (1/10) into the formula for N
= 100 + 4 (23.026) + 400*(e^(23.026)

Answer 13

ohhh is that it? omg i am such a dumb

Answer 14

sorry i made a mistake in the last part its
100 + 4(23.026) + 400e^(-23.026/10)

Answer 15

and then do i sub the number in to N again to know when it occur?

Answer 16

no when this occurs will be
1986 + 23.026
which will be in the year 2009

Answer 17

ok?

Answer 18

sorry - gotta go right now

Answer 19

thank you anyways!

Answer 20

btw what will be the date..

Answer 21

@sirm3d can you help me?

Answer 22

did it say what t represents?

Answer 23

nah but i calculated t=23.0259

Answer 24

t in years?

Answer 25

yeh and it starts from jan 1st 1986.
can you calculate the month and date as well?

Answer 26

assuming t = 23.059 years, convert that to years+days. count the number of days from Jan 1 1986 to get the approximate date (month, day, year).

Answer 27

0.059 yr x (365 days/1yr) = 21.535 days ~ 22 days
that date would be Jan 23, 2009.
i didn't check your solution if it was correct. i just assumed and showed you the computation for the nearest date the minimum would occur.

Answer 28

thank you so much your help cleared my confusion! :)

Answer 29

yw. ^^