Question

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

Answer 1

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