Question

12 a population of bacteria has an average growth rate of 2%. the formula for the growth of the bacteria’s population is $a = p_0 cdot 1.02^t$, where $p_0$ is 200 bacteria, about how many bacteria will there be after 100 hours? a 1,449 b 272 c 7 d 20,000

Explanation:

Step1: Identify given values

$P_0 = 200$, growth factor $=1.02$, $t=100$

Step2: Substitute into growth formula

$A = 200 \times 1.02^{100}$

Step3: Calculate $1.02^{100}$

$1.02^{100} \approx 7.2446$

Step4: Compute final population

$A = 200 \times 7.2446 = 1448.92$

Answer:

A. 1,449