Question

a population of grasshoppers quadruples in 20 days. assuming exponential growth, if the present population is 40 million, what will it be in 50 days. answer by first finding the number of ghoppers as a function of time. y=y0e^kt.

Answer 1

I devided
50 by 20 and got 2.5
than I multiplied 40 by 4 because I am qudrupaling it
40 times 4+40 times 4+40 times 2:

this is because you quadrupal it 2.5 times
so it would be:

160+160+80= 400
400 million grasshoppers

Answer 2

hope this helps:D

Answer 3

thank you!

Answer 4

your welcome:D

Answer 5

lets try this:
\[y=y_0e^{kt} \] \[y_0=40\]so you have
\[y=40e^{kt}\]

Answer 6

you do not know k, but you know that when t = 20, y=160 (quadruples) so we write
\[160=40e^{20k}\] and solve for k

Answer 7

first step divide by 40, it was unimportant in any case
\[4=e^{20k}\]
\[ln(4)=20k\]
\[k=\frac{ln(4)}{20}=.0693\]rounded

Answer 8

i love how helpful you are thank you so much

Answer 9

now we go back to the formula and have \[y=40e^{.0693t}\] replace t by 50 to get \[y=40e^{.0693\times 50}=40e^{3.46574}=40\times 32=1280\]\]

Answer 10

my answer may be off so let me check it

Answer 11

ok

Answer 12

i think i made a calculation error somewhere but it is certainly not the answer you were given earlier. doubles every twenty days and when you start counting you have 40 so in 20 days you have 80 and then in another 20 days (40 days later) you have 160

Answer 13

oh wait. quadruples! ok you start counting you have 40

Answer 14

yeah i got 160 when i tried on my own, i just got confused

Answer 15

yeah i got 160 when i tried on my own, i just got confused

Answer 16

yeah i got 160 when i tried on my own, i just got confused

Answer 17

in twenty day s you have 160
in another 20 day you have 640

Answer 18

so where do i plug that in?

Answer 19

so where do i plug that in?

Answer 20

so where do i plug that in?

Answer 21

ok i was right.

Answer 22

everything i wrote was correct.

Answer 23

we can do it the easy way without solving like we did, although that is what they want you to do

Answer 24

first find k, and then replace t by 50

Answer 25

it is all correct. but lets do it the easy way without all that. you know it quadruples every 20 days. so another formula you can use is \[40\times 4^{\frac{t}{20}}\]

Answer 26

now just replace t by 50 and you get
\[40\times 4^{\frac{50}{20}}=40\times 4^{\frac{5}{2}}\]

Answer 27

\[4^{frac{5}{2}}=\sqrt{4^5}=2^5=32\]

Answer 28

and \[32\times= 1280\]

Answer 29

i meant 32*40=1280

Answer 30

either way that is the correct answer

Answer 31

okay makes sense! thanks again

Answer 32

welcome