To model the growth of bacteria in a colony that begins with a single cell and doubles in size every hour, we need to use an exponential equation. This type of equation has the general form:
[tex]\[ A(b)^x \][/tex]
where:
- [tex]\( A \)[/tex] is the initial amount (the initial number of bacteria),
- [tex]\( b \)[/tex] is the base of the exponential expression (the growth factor),
- [tex]\( x \)[/tex] is the time in hours.
Let's identify and fill in the values of [tex]\( A \)[/tex] and [tex]\( b \)[/tex] based on the given conditions:
1. Initial Amount ([tex]\( A \)[/tex]): Since the colony starts with a single cell, [tex]\( A = 1 \)[/tex].
2. Growth Factor ([tex]\( b \)[/tex]): The bacteria double in size every hour, which means the number of bacteria multiplies by 2 each hour. Thus, [tex]\( b = 2 \)[/tex].
Given these values, the exponential expression to model the number of bacteria after [tex]\( x \)[/tex] hours is:
[tex]\[ 1(2)^x \][/tex]
Hence, the values are:
- [tex]\( A = 1 \)[/tex]
- [tex]\( b = 2 \)[/tex]
Therefore, the exponential expression to model the bacterial count in the dish after [tex]\( x \)[/tex] hours of growth is:
[tex]\[ 1 * (2)^x \][/tex]
