Question

1. (l4) a sample of bacteria was placed in a petri dish. the number of bacteria changes exponentially over time. the graph describes the number of bacteria over time.

a) state the domain of the graph of the function (context and type of number).
b) write an explicit function that models the relationship.

Explanation:

Step1: Identify domain context

The graph represents time in hours for bacteria growth.

Step2: Determine domain type

Time starts at 0 and can be any non - negative real number. So the domain in context is time of bacteria growth and type is non - negative real numbers.

Step3: Find the explicit function

The general form of an exponential function is $f(x)=ab^{x}$. When $x = 0$, $f(0)=ab^{0}=a$. From the table, when $x = 0$, $f(0)=50$, so $a = 50$.
To find $b$, we know that when $x = 1$, $f(1)=ab^{1}$. Since $a = 50$ and $f(1)=60$, then $50b=60$, so $b=\frac{60}{50}=1.2$. The explicit function is $f(x)=50\times(1.2)^{x}$.

Answer:

a) Context: Time of bacteria growth; Type: Non - negative real numbers.
b) $f(x)=50\times(1.2)^{x}$