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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.

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  1. anonymous
    • 5 years ago
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    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

  2. anonymous
    • 5 years ago
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    hope this helps:D

  3. anonymous
    • 5 years ago
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    thank you!

  4. anonymous
    • 5 years ago
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    your welcome:D

  5. anonymous
    • 5 years ago
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    lets try this: \[y=y_0e^{kt} \] \[y_0=40\]so you have \[y=40e^{kt}\]

  6. anonymous
    • 5 years ago
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    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

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

  8. anonymous
    • 5 years ago
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    i love how helpful you are thank you so much

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

  10. anonymous
    • 5 years ago
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    my answer may be off so let me check it

  11. anonymous
    • 5 years ago
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    ok

  12. anonymous
    • 5 years ago
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    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

  13. anonymous
    • 5 years ago
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    oh wait. quadruples! ok you start counting you have 40

  14. anonymous
    • 5 years ago
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    yeah i got 160 when i tried on my own, i just got confused

  15. anonymous
    • 5 years ago
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    yeah i got 160 when i tried on my own, i just got confused

  16. anonymous
    • 5 years ago
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    yeah i got 160 when i tried on my own, i just got confused

  17. anonymous
    • 5 years ago
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    in twenty day s you have 160 in another 20 day you have 640

  18. anonymous
    • 5 years ago
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    so where do i plug that in?

  19. anonymous
    • 5 years ago
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    so where do i plug that in?

  20. anonymous
    • 5 years ago
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    so where do i plug that in?

  21. anonymous
    • 5 years ago
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    ok i was right.

  22. anonymous
    • 5 years ago
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    everything i wrote was correct.

  23. anonymous
    • 5 years ago
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    we can do it the easy way without solving like we did, although that is what they want you to do

  24. anonymous
    • 5 years ago
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    first find k, and then replace t by 50

  25. anonymous
    • 5 years ago
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    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 \[40\times 4^{\frac{t}{20}}\]

  26. anonymous
    • 5 years ago
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    now just replace t by 50 and you get \[40\times 4^{\frac{50}{20}}=40\times 4^{\frac{5}{2}}\]

  27. anonymous
    • 5 years ago
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    \[4^{frac{5}{2}}=\sqrt{4^5}=2^5=32\]

  28. anonymous
    • 5 years ago
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    and \[32\times= 1280\]

  29. anonymous
    • 5 years ago
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    i meant 32*40=1280

  30. anonymous
    • 5 years ago
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    either way that is the correct answer

  31. anonymous
    • 5 years ago
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    okay makes sense! thanks again

  32. anonymous
    • 5 years ago
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    welcome

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