Question

Data from an independent research company found that the annual cost per worker for insurance​ (health, life,​ liability, etc.) was increasing according to the function f (x )equals 67.81 e Superscript 0.44 x Baseline comma where f (x )is the cost in dollars per year at time​ x, and x is the number of years measured from the beginning of the year 1997. That​ is, x equals 0 corresponds to the start of 1997. Find the total increase in costs during the next 5 ​years, beginning in 1997.

Answer 1

Answer:

The cost per worker goes in five years from $67.81 at 1997, to $394.14 in 2001. It is an increase of $326.33 (481%).

$f(0)=67.81e^{0.44\cdot 0}=67.81*1=67.81\\\\f(1)=67.81e^{0.44\cdot1}=67.81*1.553=105.29\\\\f(2)=67.81e^{0.44\cdot2}=67.81*2.411=163.48\\\\f(3)=67.81e^{0.44\cdot3}=67.81*3.743=253.84\\\\f(4)=67.81e^{0.44\cdot4}=67.81*5.812=394.14$

Step-by-step explanation:

The annual cost per worker is modeled by the function:

$f(x)=67.81e^{0.44\cdot x}$

where x = years from 1997.

We have to calculate the cost per worker from 1997 to 2001, according to the function f(x).

We have:

$f(0)=67.81e^{0.44\cdot 0}=67.81*1=67.81\\\\f(1)=67.81e^{0.44\cdot1}=67.81*1.553=105.29\\\\f(2)=67.81e^{0.44\cdot2}=67.81*2.411=163.48\\\\f(3)=67.81e^{0.44\cdot3}=67.81*3.743=253.84\\\\f(4)=67.81e^{0.44\cdot4}=67.81*5.812=394.14$

The cost per worker goes in five years from $67.81 at 1997, to $394.14 in 2001. It is an increase of $326.33 (481%).