How to get around an overflow error in Ti-84 plus calculator?

so i'm having a problem where i'm trying to find the answer to this equation

Ŷ = (10^-509.0738)(2020^158.0975)

The problem is that when i plug it into my calculator, it says an overflow error. Is there anyway to get around this or is there an alternative way of solving it?

Thanks.

3 Answers

Relevance
  • ?
    Lv 7
    9 years ago
    Favorite Answer

    Yeah, the TI-84 Plus can only handle a maximum exponent of 99. Anything over that will get you Err:Overflow.

    Given:

    y = (10^-509.0738)(2020^158.0975)

    Take the appropriate logs:

    log y = log(10^-509.0738)(2020^158.0975))

    log y = log(10^-509.0738) + log(2020^158.0975)

    log y = -509.0738 + 158.0975log(2020)

    log y = -509.0738 + 522.5677881

    log y = -509.0738 + 522.5677881

    log y = 13.49

    y = 10^13.49

    y ≈ 3.1188 × 10^13

  • 9 years ago

    Yes. Use base 10 logarithms, plus some pencil and paper (or memory registers).

    log Ŷ = -509.0738 + (log 2020)*158.0975

    = 13.493988

    The integer part of your answer is the power of 10 of the answer in scientific notation, and the decimal fraction is the base-10 log of the significant digits.

    Ŷ = 3.118804 x 10^13

    That works because 13.493988 = 13 + 0.493988

    If you got a negative answer, like -13.493988, then this is not -13 + 0.493988. Instead you have

    -13 - 0.493988 = -14 + 1 - 0.493988 = -14 + 0.506012

    1/Ŷ is then 3.206358 x 10^-14

    In this problem, the integer part was small enough that you could just use your 10^x or x^y function on the calculator. In other problems, the integer part might be too large to represent, so you'd manually separate the integer and fraction parts of the logarithm to get a pencil-and-paper answer in scientific notation.

  • 3 years ago

    i've got used the two. they are rather much precisely an identical. The purposes are an identical, the layouts are an identical, and from a functional perspective, each thing is an identical. the only transformations are aesthetic (eighty 4 is extra alluring), and the reminiscence on the eighty 4 is larger, meaning that the eighty 4 is speedier, too, yet except you're appearing some extreme calculations or apps, it is not possibly substantive. The eighty 4 additionally comes with extra apps via default, and it comes with a cable and utility so as which you will connect it on your computing gadget. it particularly is a sprint pricier, yet not via too lots. in case you like an eighty 4, sure, you could definitely get it particularly of an eighty 3. Functionally, they are an identical. The keys are an identical and each thing; they only seem distinctive, yet each thing's interior an identical place, and each thing works an identical way.

Still have questions? Get your answers by asking now.