Repeated multiplication over equal time intervals signals an exponential model. Find the starting amount, the factor applied each interval, and the number of intervals that have passed. That interval count becomes the exponent. If the factor applies every several hours, using the hours directly as the exponent makes the model grow too fast.
Hints
- Hint 1
The initial value is the amount when . Here, time starts at 9:00 a.m. What cell count must the model give at that moment?
- Hint 2
A growth factor is the number you multiply by after one full interval. Doubling means multiplying the current cell count by . How long does one doubling interval last?
- Hint 3
The exponent counts how many times the growth factor has been applied. After one full doubling interval, it should be . What expression equals when ?
Step-by-step
Build the model from the doubling interval
Step 1Identify the starting amount
No Desmos needed. The starting count and doubling interval determine the model directly. At 9:00 a.m., no time has passed, so . The initial value is the count at that time: . That makes the number in front of the power.
- Step 2
Translate doubling into a multiplier
The culture doubles every 6 hours, so after one six-hour interval its count is multiplied by : . The growth factor is , not ; multiplying by would increase a count by only .
- Step 3
Count the doubling intervals
The exponent must count six-hour intervals, so it is . At , that exponent is , giving exactly one doubling. The exponent counts doubling intervals, not individual hours. Using alone would apply the factor every hour.
- Step 4
Write the cell-count model
Put the starting count, growth factor, and interval count together: . This gives the number of infected cells hours after 9:00 a.m. Choice B.