Question

below is a table showing the number of bacteria in a culture at different times.

which equation best represents the growth of bacteria over time?

\\(y = 100 \cdot 1.1^x\\)
\\(y = 50 \cdot 1.5^x\\)
\\(y = 75 \cdot 2^x\\)
\\(y = 50 \cdot 1.25^x\\)

Explanation:

Identify the initial value

$$ y(0) = 50 \implies a = 50 $$

Determine the growth factor

$$ b = \frac{y(1)}{y(0)} = \frac{75}{50} = 1.5 $$

Formulate the exponential equation

$$ y = 50 \cdot 1.5^x $$

Answer:

• (A) \(y = 100 \cdot 1.1^x\)
• (B) \(y = 50 \cdot 1.5^x\) (Correct answer)
• (C) \(y = 75 \cdot 2^x\)
• (D) \(y = 50 \cdot 1.25^x\)