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Exponential model word problem: bacteria growth

Sal evaluates an exponential function at a specific value in order to answer a question about an exponential model.

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  • hopper cool style avatar for user Bob The Zealot
    Do bacteria actually produce future generations exponentially like it is described in the problem?
    (9 votes)
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    • purple pi purple style avatar for user Adnan Akhundov
      I think they do, pretty much like any other species. However, in case of bacteria cumulative outcome of this reproduction is very substantial and visible, as (under favourable conditions) they produce subsequent generations very frequently. Much more frequently than previous generations fade away.
      (9 votes)
  • blobby green style avatar for user shawnlau23
    Wondering why this video is included in the Algebra II logarithms section. The problem doesn't require the use of logarithms.
    (6 votes)
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    • stelly blue style avatar for user Kim Seidel
      You're right that logs were not needed. This is because you were given a value for t. If the problem had asked you to find "t" when b(t) = 10,240, then you would have needed logarithms.
      This is likely why the video is in the logarithm section.
      (3 votes)
  • duskpin ultimate style avatar for user Ghassan O. Najjar
    At where did 2^5 come from?
    (2 votes)
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  • male robot hal style avatar for user svlohit2012
    Shouldn't you divide by 120 for the last step?
    (2 votes)
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  • blobby green style avatar for user allkle22
    What do you do if the e is the t?
    (2 votes)
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  • blobby green style avatar for user Clarice
    Suppose that a computer program is able to sort n input values in k x n^(1.5) microseconds. Observations show that it sorts a million values in half a second. Find the value of k.

    May I ask how will you set up an equation for this?
    (1 vote)
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    • primosaur tree style avatar for user Bradley Reynolds
      The word problem states that the computer can sort n values in k * n^(1.5) microseconds. This gives us an equation of time to sort = k * n^(1.5). We are then given that it can sort one million values in half a second, this means our time would equal 500,000 microseconds (one million microseconds in a second). So we can then have an equation of 500,000 = k * (1,000,000)^1.5. From here the rest of the problem is simple algebra and you get your answer of k = 0.0005.
      (3 votes)
  • blobby green style avatar for user stephanyarycha169
    how to solve this question sir?
    The number of cell double after each process of cell division every 2 hours. If there are 120 bacteria initially, how many bacteria will be there after one and half day?
    (1 vote)
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  • primosaur ultimate style avatar for user NEOVISION
    10^d/2 = 16,000

    to

    d/2 =log(16,000)

    shouldn't it be division insted of multiplication ?

    so d/2 = 16,000 / 10

    = d/2 = log(1/10) (16,000) (maybe)

    why? I'm confused, can anybody explain it(please) ?
    (1 vote)
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  • boggle blue style avatar for user sanangelo9250
    Hi Thank you for the awesome videos.
    I just have one question. When rounding to the nearest thousandth and hundredth, how do i know when to round up?
    (1 vote)
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  • blobby blue style avatar for user Lizzie Bryce
    I am attempting to find the y intercept of the equation
    y = 2(2^(x+1)) + 1 but I cannot figure it out because I cannot isolate 2^(x+1) and another single variable to substitute into a logarithmic equation with the + 1 on the end.
    (1 vote)
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Video transcript

- The bacteria in a Petri dish culture are self-duplicating at a rapid pace. The relationship between the elapsed time T, in minutes, and the number of bacteria, B of T, in the Petri dish is modeled by the following function. And we see it's an exponential model here. How many bacteria will make up the culture after 120 minutes? So, really they just want to say, well what is B of 120 going to be? And so it's going to be 10 times two to the 120 divided by 12th power. So, this is going to be equal to 10 times two to the, 120 divided by 12 is, 10th power. So this is going to be equal to 10 times, two to the 10th power is 1,024. If you want to verify that, you can say, well two to the 5th is equal to 32, and so two to the 10th is going to be two to the 5th times two to the 5th. And 32 times 32 is... Let's see, 64. Zero. So, Let's see we're gonna have... Sorry, three times 32 is 96. Let's see you have a four and 12, 1024. So this is gonna be 1024. 10 times that is going to be equal to one zero two four zero. So, 10,200... 10,240 bacteria, and we're done.