anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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
anonymous
  • anonymous
hope this helps:D
anonymous
  • anonymous
thank you!

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anonymous
  • anonymous
your welcome:D
anonymous
  • anonymous
lets try this: \[y=y_0e^{kt} \] \[y_0=40\]so you have \[y=40e^{kt}\]
anonymous
  • anonymous
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
anonymous
  • anonymous
first step divide by 40, it was unimportant in any case \[4=e^{20k}\] \[ln(4)=20k\] \[k=\frac{ln(4)}{20}=.0693\]rounded
anonymous
  • anonymous
i love how helpful you are thank you so much
anonymous
  • anonymous
now we go back to the formula and have \[y=40e^{.0693t}\] replace t by 50 to get \[y=40e^{.0693\times 50}=40e^{3.46574}=40\times 32=1280\]\]
anonymous
  • anonymous
my answer may be off so let me check it
anonymous
  • anonymous
ok
anonymous
  • anonymous
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
anonymous
  • anonymous
oh wait. quadruples! ok you start counting you have 40
anonymous
  • anonymous
yeah i got 160 when i tried on my own, i just got confused
anonymous
  • anonymous
yeah i got 160 when i tried on my own, i just got confused
anonymous
  • anonymous
yeah i got 160 when i tried on my own, i just got confused
anonymous
  • anonymous
in twenty day s you have 160 in another 20 day you have 640
anonymous
  • anonymous
so where do i plug that in?
anonymous
  • anonymous
so where do i plug that in?
anonymous
  • anonymous
so where do i plug that in?
anonymous
  • anonymous
ok i was right.
anonymous
  • anonymous
everything i wrote was correct.
anonymous
  • anonymous
we can do it the easy way without solving like we did, although that is what they want you to do
anonymous
  • anonymous
first find k, and then replace t by 50
anonymous
  • anonymous
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 \[40\times 4^{\frac{t}{20}}\]
anonymous
  • anonymous
now just replace t by 50 and you get \[40\times 4^{\frac{50}{20}}=40\times 4^{\frac{5}{2}}\]
anonymous
  • anonymous
\[4^{frac{5}{2}}=\sqrt{4^5}=2^5=32\]
anonymous
  • anonymous
and \[32\times= 1280\]
anonymous
  • anonymous
i meant 32*40=1280
anonymous
  • anonymous
either way that is the correct answer
anonymous
  • anonymous
okay makes sense! thanks again
anonymous
  • anonymous
welcome

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