To answer the question, let's analyze the given function:
[tex]\[ f(t) = 1.5 \cdot (0.90)^t \][/tex]
Here, [tex]\( t \)[/tex] represents the number of years since the company revised the benefits package, and [tex]\( f(t) \)[/tex] describes the number of employees in thousands.
The function is of the form:
[tex]\[ f(t) = a \cdot (b)^t \][/tex]
where [tex]\( a \)[/tex] is the initial amount (in this case, 1.5 thousand employees), and [tex]\( b \)[/tex] is the base of the exponential function. The base [tex]\( b \)[/tex] determines the rate of change:
1. If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
2. If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
In our function, the base is [tex]\( 0.90 \)[/tex], which means that every year, the number of employees is multiplied by 0.90.
To understand the percentage change:
- The number [tex]\( b = 0.90 \)[/tex] indicates that each year, the number of employees is 90% of what it was the previous year.
- This also means there is a reduction of [tex]\( 100\% - 90\% = 10\% \)[/tex] each year.
Therefore, the number of employees is decreasing by 10% every year.
Thus, the correct answer is:
B. The number of employees is decreasing by 10% every year.
