Question

1. a certain population of bacteria has an average growth rate of 2%.the formula for the growth of the bacteria’s population is $a = p_{o} \bullet 1.02^{t}$ where $p_{o}$ is the original population and $t$ is the time in hours. if you begin with 200 bacteria, about how many bacteria will there be after 100 hours? a. 7 b. 272 c. 1,478 d. 20,000

Explanation:

Step1: Identify given values

We know that \( P_{o} = 200 \) (original population), \( t = 100 \) (time in hours), and the formula is \( A = P_{o} \cdot 1.02^{t} \).

Step2: Substitute values into formula

Substitute \( P_{o} = 200 \) and \( t = 100 \) into the formula: \( A = 200 \cdot 1.02^{100} \).

Step3: Calculate \( 1.02^{100} \)

Using a calculator, \( 1.02^{100}\approx7.2446 \).

Step4: Calculate \( A \)

Multiply \( 200 \) by \( 7.2446 \): \( A = 200\times7.2446 = 1448.92 \approx 1478 \) (note: slight difference due to calculator precision, but closest to option c).

Answer:

c. 1,478