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The following function describes the number of employees working at a company (in thousands), where [tex]\( t \)[/tex] represents the number of years since the company revised the benefits package:
[tex]\[ f(t) = 1.5(0.90)^t \][/tex]

A. The number of employees is increasing by 50% every year.
B. The number of employees is decreasing by 10% every year.
C. The number of employees is decreasing by 90% every year.
D. The number of employees is increasing by 90% every year.



Answer :

GinnyAnswer
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.

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