Writing and Solving Exponential Equations: Tutorial

The researcher wants to calculate the bacterial count in the dish after [tex]\( x \)[/tex] hours of growth.

Fill in the values of [tex]\( A \)[/tex] and [tex]\( b \)[/tex] to write an exponential expression to model the number of bacteria in a colony that begins with a single cell and doubles in size every hour.

[tex]\[ A(b)^x \][/tex]

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Answer :

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]