suppose you start with 75 grams of the substance after 2.5 min you have grams left. how much longer will it take you have half remaining
How many after 2.5 ?
x = Xi e^-kt
x = 75 e^-2.5 k
ln(x/75) = -2.5 k
k = ln(x/75)/(-2.5) solve for k
so
ln .5 = -k t
solve for t
Oh, yes, the diff eq which everyone already knows the solution for
da/dt = -ka
da/a = - k dt
ln a = -kt
a = A e^-kt
To determine how much of the substance is left after 2.5 minutes, we need to know the rate at which it is being depleted. Without this information, we won't be able to provide an accurate answer. However, I can explain the general concept of finding the remaining amount and how long it takes to have half remaining.
To calculate the remaining amount, you need to know the rate of decay or depletion of the substance per unit of time. This is usually expressed as a percentage or a ratio. Let's assume the depletion rate is constant and represented as a percentage.
To find the remaining amount after 2.5 minutes, you would multiply the initial amount (75 grams) by the ratio of the remaining amount after 2.5 minutes. If the depletion rate is given as a percentage, you would convert it to a decimal by dividing by 100.
Remaining amount = Initial amount x (1 - depletion rate)
Next, to find out how much longer it would take to have half remaining, we'll use the same concept. We'll solve for the time when the remaining amount is half of the initial amount (37.5 grams) using the formula above.
Now, without the specific depletion rate, I'm unable to calculate the exact answers for you. However, with the given information and the formula provided, you should be able to calculate the answers if you have the depletion rate.