Andrew measures the amount of a very unstable substance to be 100 moles. The half-life of this substance is 3 days (after 3 days, half is gone).
Write an exponential function that models this situation where y is the amount of substance and x is time in days.
Thank you for reading!
To write an exponential function that models this situation, we can use the formula for exponential decay:
y = A * (1/2)^(x/h)
In this formula, y represents the amount of the substance at any given time x, A represents the initial amount of the substance, and h represents the half-life of the substance.
In this case, the initial amount of the substance is 100 moles and the half-life is 3 days. Therefore, we can substitute these values into the formula:
y = 100 * (1/2)^(x/3)
This exponential function will model the situation where y is the amount of substance and x is the time in days.
To write an exponential function that models this situation, we can use the general form of an exponential function:
y = a * b^x
In this case, a represents the initial amount of the substance, which is 100 moles. The half-life of the substance is 3 days, which means that after 3 days, the amount is halved. Therefore, the base, b, will be equal to (1/2) because the amount is halved every 3 days.
So, the exponential function that models this situation is:
y = 100 * (1/2)^x