Question

4
select the correct answer.
the following function describes the number of employees working at a company, in thousands, where t represents the number of years since the company revised the benefits package.
$f(t) = 1.5(0.90)^t$
a. the number of employees is increasing by 90% every year.
b. the number of employees is increasing by 50% every year.
c. the number of employees is decreasing by 90% every year.
d. the number of employees is decreasing by 10% every year.

Explanation:

Step1: Recall exponential decay formula

The general form of an exponential function is \( f(t) = a(b)^t \), where \( a \) is the initial amount, and \( b \) is the base. If \( 0 < b < 1 \), it represents exponential decay. The decay rate \( r \) is related to \( b \) by \( b = 1 - r \).

Step2: Analyze the given function

For the function \( f(t) = 1.5(0.90)^t \), the base \( b = 0.90 \). Since \( 0.90 < 1 \), this is an exponential decay function.

Step3: Calculate the decay rate

Using the formula \( b = 1 - r \), we substitute \( b = 0.90 \):
\( 0.90 = 1 - r \)
Solving for \( r \):
\( r = 1 - 0.90 = 0.10 \), which is 10%. So the number of employees is decreasing by 10% every year.

Answer:

D. The number of employees is decreasing by 10% every year.