For selected years, the national health care expenditure, in billion of dollors can be modelled by H=29.57e^0.0970t, remains acurate, how long will it be before national health expenditure reach 6000 billion dollors?

The correct answer is 54.76 years.

Step-by-step explanation:

The national health care expenditure (H) , in billion of dollars is modeled by

H = 29.57 × .

To measure the time before which national health expenditure reach 6000 billion dollars.

Thus putting the value of H = 6000 in the above modeled equation we get,

⇒ 6000 = 29.57 ×

⇒ =

⇒ 202.908 =

Taking logarithm with the base of e (㏑) both sides we get,

⇒ ㏑ 202.908 = ㏑

⇒ ㏑ 202.908 = 0.0970 × t

⇒ 0.0970 × t = 5.312

⇒ t =

⇒ t = 54.76.

Thus the total time required before which national health expenditure reach 6000 billion dollars is 54.76 years.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: