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:

Step1: Identify initial - value

When \(t = 0\), from the graph, the population of bacteria \(f(0)=10\). So the general form of an exponential - growth function is \(f(t)=a\cdot b^{t}\), where \(a\) is the initial value. Here \(a = 10\).

Step2: Check the growth - factor

Let's take two points \((t_1,f(t_1))\) and \((t_2,f(t_2))\) from the graph. For example, when \(t = 1\), \(f(1)\approx14\) and when \(t = 0\), \(f(0)=10\). The growth factor \(b=\frac{f(1)}{f(0)}=\frac{14}{10}=1.4\).

Answer:

\(f(t)=10(1.4)^{t}\)