Question

the graph shows the population of a bacteria in an experiment, measured every hour.

which function represents the population of the bacteria after \\(t\\) hours?

\\(f(t) = 10(1.4)^t\\)
\\(f(t) = 10(2.0)^t\\)
\\(f(t) = 14(1.4)^t\\)
\\(f(t) = 14(2.0)^t\\)

Explanation:

Identify the initial value from the graph

Using the Y-Intercept and Graph Interpretation knowledge points

$$ f(0) = 10 $$

Determine the growth factor

Using the Exponential Functions and Exponential Modeling knowledge points

$$
LATEXBLOCK0
$$

Formulate the final function

Using the Exponential Functions knowledge point

$$ f(t) = 10(1.4)^t $$

Answer:

• (A) \(f(t) = 10(1.4)^t\) (Correct answer)
• (B) \(f(t) = 10(2.0)^t\)
• (C) \(f(t) = 14(1.4)^t\)
• (D) \(f(t) = 14(2.0)^t\)