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Math Help - Exponential equation help

  1. #1
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    Exponential equation help

    Can someone help tell me how to do this? Thanks in advance.

    At any time t>0, the growth of a bacteria culture is growing exponentially and y represents the amount of bacteria present at any time t. The initial population (t=0) is 1000 and the population triples during the first 5 days. Write an expression for y at any time t≥0.
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  2. #2
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    Sorry for the double post, but could someone help me?

    I got an answer of (4.5735^x)+999. Is that correct?
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  3. #3
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    Quote Originally Posted by Cursed View Post
    Can someone help tell me how to do this? Thanks in advance.

    At any time t>0, the growth of a bacteria culture is growing exponentially and y represents the amount of bacteria present at any time t. The initial population (t=0) is 1000 and the population triples during the first 5 days. Write an expression for y at any time t≥0.
    y = y_0e^{\lambda t}

    We know that y_0 = 1000 and that in t = 5 days the population triples. So
    3000 = 1000e^{5 \lambda}

    3 = e^{5\lambda}

    ln(3) = 5 \lambda

    \lambda = \frac{ln(3)}{5} \approx 0.219722

    So
    y = 1000e^{0.219722 t}

    This is an acceptable answer, but we can do a bit better if you wish to do a little more algebra.

    Recall \lambda = \frac{ln(3)}{5}

    So
    y = 1000e^{t \cdot ln(3)/5}

    Using exponent properties:
    y = 1000 \left ( e^{ln(3)} \right ) ^{t/5}

    y = 1000 \cdot 3^{t/5}

    -Dan
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