Question

algebra: concepts and connections - plc
exponential growth functions
anticipating exponential growth
a scientist is studying a certain strain of bacteria that grows at an exponential rate, doubling each cell every 5 minutes.
imagine that 1 bacteria cell is placed in this glass bottle at 10:00 a.m.
at 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. how many cells will be in the bottle at 10:15 a.m.?

Explanation:

Step1: Identify time intervals

Time between 10:05 a.m. and 10:15 a.m. is $10:15 - 10:05 = 10$ minutes. With a 5-minute doubling period, number of intervals: $\frac{10}{5}=2$

Step2: Apply exponential growth formula

Exponential growth formula: $N = N_0 \times 2^t$, where $N_0=2$ (initial cells), $t=2$ (doubling intervals)
Expression: $N = 2 \times 2^2$

Step3: Calculate final cell count

First compute $2^2=4$, then multiply by initial count: $2 \times 4=8$

Answer:

8