Question

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?

Answer 1

Answer:

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 × $e^{0.0970t}$.

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 × $e^{0.0970t}$

⇒ $\frac{6000}{29.57}$ = $e^{0.0970t}$

⇒ 202.908 = $e^{0.0970t}$

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

⇒ ㏑ 202.908 = ㏑ $e^{0.0970t}$

⇒ ㏑ 202.908 = 0.0970 × t

⇒ 0.0970 × t = 5.312

⇒ t = $\frac{5.312}{0.0970}$

⇒ t = 54.76.

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