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22 February, 13:25

Bytecoin is a new cryptocurrency that is currently valued at $243 per coin. You want to make an investment and purchase 1 Bytecoin and cash out when its value reaches $1,000. Over the last 12 months, you ve seen the value of the Bytecoin grow exponentially at a rate of 15% per month! You want all of your friends and family to invest with you, but you need to make predictions about how long it will take for your $243 investment to earn $1,000. Write an exponential equation in the form y = a * b ^ x and explain what a and b represent

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  1. 22 February, 16:20
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    Step-by-step explanation:

    The growth rate of the coin is exponential. We would apply the formula for exponential growth which is expressed as

    y = ab^x

    y = b (1 + r) ^ t

    Where

    y represents the value of the coin after x months.

    x represents the number of months.

    a represents the initial value of the coin.

    b represents rate of growth.

    From the information given,

    a = 243

    b = 1 + 15/100 = 1 + 0.15 = 1.15

    Therefore, the exponential expression to determine the number of months, x it will take for the coin to attain a certain value, y is expressed as

    y = 243 (1.15) ^x

    If y = 1000, it means that

    1000 = 243 (1.15) ^x

    1000/243 = 1.15^x

    4.115 = 1.15^x

    Taking log of both sides, it becomes

    log 4.115 = xlog1.15

    0.614 = 0.061x

    x = 0.614/0.061

    x = 10 months

    It will take 10 months
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