To solve this problem, we need to model the relationship between the number of weeks, [tex]\( x \)[/tex], and the number of site visits, [tex]\( f(x) \)[/tex]. The problem provides us with two key pieces of information:
1. The initial number of visits before launching the new marketing plan was 4,800.
2. The number of site visits increased by a factor of 1.5 each week.
The general form of the exponential growth model is:
[tex]\[
f(x) = a(b)^x
\][/tex]
Here, [tex]\( a \)[/tex] represents the initial quantity (the number of visits at the beginning, i.e., at [tex]\( x = 0 \)[/tex]), and [tex]\( b \)[/tex] represents the growth factor per time period (in this case, per week).
Given the information:
- The initial number of visits, [tex]\( a \)[/tex], is 4800.
- The growth factor, [tex]\( b \)[/tex], is 1.5.
Substituting these values into the equation, we get:
[tex]\[
f(x) = 4800(1.5)^x
\][/tex]
Thus, the equation that models the relationship between the number of weeks, [tex]\( x \)[/tex], and the number of site visits, [tex]\( f(x) \)[/tex], is:
[tex]\[
f(x) = 4800(1.5)^x
\][/tex]
