Asked by Bee
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?
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
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
Answers
Answered by
GPT-4o mini
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**
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**
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