In an exponential decay model, the exponent counts how many equal time intervals have passed. If a question changes the input from days to hours, keep the starting mass and decay factor, but express the halving interval in hours. Putting hours directly into an exponent built for days makes the sample decay too fast.
Hints
- Hint 1
The exponent reaches after days, so the factor has been applied once. One halving takes days. How long is that in hours?
- Hint 2
An exponent counts completed intervals. Once you know how many hours one halving takes, divide by that number so the exponent becomes after exactly one halving.
Step-by-step
Convert the halving interval to hours
Step 1Read the halving interval
In the given model, the exponent reaches when . So the mass is multiplied by every 18 days. To see that in Desmos, temporarily set the initial mass to : type , enter the given function, then type . Desmos shows , one-half of the starting mass.
- Step 2
Convert one halving interval to hours
Each day has hours, so 18 days contains hours. Type into Desmos; it shows . So one halving takes hours, not hours.
- Step 3
Write the model with hours as the input
The exponent must count halving intervals, so divide the hours passed by the hours in one interval:
At , the exponent is , so the mass is half the initial mass. Change the time unit in the exponent, not the decay factor. This gives the mass hours after the initial measurement. Choice B.