A colony of approximately 2,000,000 bacteria is treated with an experimental antibiotic. Every hour, the population decreases 8%. Which function models the population after t hours?

Question

y = a * (1 plus/minus r)'

y = a * (1 + r/n) ^ n

y =a0^ prime prime

f(t) = 2000000 * (0.92) ^ t

f(t) = 2000000 * (1.08) ^ t

f(t) = 2000000 * (0.08) ^ t

Df f(t) = 2000000t ^ 0.08

Answer 1

To model the population of bacteria that decreases by 8% every hour, we start with the initial population and apply the decay factor.

1. The initial population \( a \) is 2,000,000.
2. Since the population decreases by 8%, the remaining population after one hour is 92% of its current value. This can be represented as \( 1 - 0.08 = 0.92 \).

The function that models the population after \( t \) hours is given by:

\[ f(t) = a \cdot (1 - r)^t \]

Substituting the values:

\[ f(t) = 2000000 \cdot (0.92)^t \]

Thus, the correct function that models the population after \( t \) hours is:

\[ f(t) = 2000000 \cdot (0.92)^t \]

So, the answer is:

f(t) = 2000000 * (0.92) ^ t