In an exponential model, the output at time is the starting amount, and dividing a later output by an earlier one gives the multiplier. Put the table into Desmos to find that ratio. Then check the time gap: the exponent counts how many gaps have passed. Using time itself as the exponent applies the multiplier too often when each gap is longer than one time unit.
Hints
- Hint 1
The initial value is the amount at time . An exponential power equals when its exponent is , so which table entry must be the number in front of the power?
- Hint 2
A multiplier compares outputs by division, not subtraction. Divide the later concentration by the earlier one, then ask how many hours passed while that multiplier took effect.
- Hint 3
The exponent counts how many times the multiplier acts. What expression equals after one full interval and after two intervals?
Step-by-step
Find the start, multiplier, and interval
Step 1Find the starting concentration
At , the table gives . The initial value is the amount at time . Since a power with exponent equals , the number in front of the exponential power must be mg/L.
- Step 2
Find the multiplier
Copy both rows into a Desmos table. Type ; the brackets select the second and first concentrations. Desmos shows . An exponential multiplier is what you multiply the previous amount by, so the concentration is multiplied by over this two-hour jump.
- Step 3
Count the two-hour intervals
The multiplier acts once every hours, so the exponent must count two-hour intervals. Divide elapsed hours by the interval length: . At , the exponent is , meaning the multiplier acts once. The exponent counts intervals, not raw time.
- Step 4
Write the model
Put the starting concentration, multiplier, and interval count together: . This starts at mg/L and gives mg/L after one two-hour interval. Choice B.