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Math Help - Exponential growth/decay

  1. #1
    Member realintegerz's Avatar
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    Aug 2008
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    Exponential growth/decay

    1. I just want to know if this equation is correct

    The # of bacteria growing in meat doubles each day while in a fridge. When you buy the meat, it contains 300 bacteria. Find a function that represents the # of bacteria in the meat after t days

    2. If an inflation rate remains at 4% a year, then the amount a dollar is worth decreases by 4% a year
    a) assume today a dollar is actually worth $1, at the stated rate of inflation, how much will this dollar be worth after 6 years
    b) find a function which describes the value of a dollar after t years

    I tried and made a function f(t) = 1 - (1/25)^t but it didnt work

    3. A yeast colony is growing exponentially. It starts with 400 individuals and 2 hours later it has 4,000. Find a function describing the amount of yeast in the colony after t hours
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  2. #2
    Member
    Joined
    Dec 2008
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    Indiana
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    Hi realintegerz,

    1.The # of bacteria growing in meat doubles each day while in a fridge. When you buy the meat, it contains 300 bacteria. Find a function that represents the # of bacteria in the meat after t days
    It is an exponential function, so it will have the form y=ab^t, where a is the initial value and b = 1+r with r being the growth rate. Now see if you can put them together.

    2. If an inflation rate remains at 4% a year, then the amount a dollar is worth decreases by 4% a year
    a) assume today a dollar is actually worth $1, at the stated rate of inflation, how much will this dollar be worth after 6 years
    b) find a function which describes the value of a dollar after t years

    I tried and made a function f(t) = 1 - (1/25)^t but it didnt work
    Similar to #1, y=ab^t is what you need. In this case your growth rate (or decay rate) " r" is going to be negetive, in particular, r=-.04.

    3. A yeast colony is growing exponentially. It starts with 400 individuals and 2 hours later it has 4,000. Find a function describing the amount of yeast in the colony after t hours
    Same idea here. You need to find a formula, y=ab^t. The information above gives two points (0, 400) and (2, 4000). You can form two equations by plugging in the points and solve a and b.
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