An exponential model multiplies a starting amount by a factor as time passes. To find the initial amount, use and evaluate the given model in Desmos. The factor tells you how the amount changes over time; it isn't the amount at the start.
Hints
- Hint 1
An initial value is the amount before any time has passed. Here, counts days after the initial measurement. What value of represents the moment that measurement was made?
- Hint 2
At the start, the exponent is . Any nonzero number to the zero power equals . What does that leave in the model?
Step-by-step
Evaluate the model at the start
Step 1Find the time of the initial measurement
The problem counts in days after the initial measurement, so at the initial measurement, . Substitute for to find the starting mass: .
- Step 2
Evaluate the starting mass
Type , then in Desmos. Desmos displays . That's because , so the daily multiplier hasn't changed the mass yet. The initial mass is milligrams. Choice D.