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anonymous
 5 years ago
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.
anonymous
 5 years ago
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.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lets try this: \[y=y_0e^{kt} \] \[y_0=40\]so you have \[y=40e^{kt}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you do not know k, but you know that when t = 20, y=160 (quadruples) so we write \[160=40e^{20k}\] and solve for k

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first step divide by 40, it was unimportant in any case \[4=e^{20k}\] \[ln(4)=20k\] \[k=\frac{ln(4)}{20}=.0693\]rounded

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i love how helpful you are thank you so much

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now we go back to the formula and have \[y=40e^{.0693t}\] replace t by 50 to get \[y=40e^{.0693\times 50}=40e^{3.46574}=40\times 32=1280\]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my answer may be off so let me check it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh wait. quadruples! ok you start counting you have 40

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i got 160 when i tried on my own, i just got confused

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i got 160 when i tried on my own, i just got confused

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i got 160 when i tried on my own, i just got confused

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in twenty day s you have 160 in another 20 day you have 640

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so where do i plug that in?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so where do i plug that in?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so where do i plug that in?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0everything i wrote was correct.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we can do it the easy way without solving like we did, although that is what they want you to do

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first find k, and then replace t by 50

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it 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 \[40\times 4^{\frac{t}{20}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now just replace t by 50 and you get \[40\times 4^{\frac{50}{20}}=40\times 4^{\frac{5}{2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[4^{frac{5}{2}}=\sqrt{4^5}=2^5=32\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and \[32\times= 1280\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0either way that is the correct answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay makes sense! thanks again
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