Write the word or phrase that best completes each statement or answers the question.
-Suppose the number of Quickie hamburgers (in millions) served yearly can be modeled by $f ( x ) = 37.8 e ^ { 0.18 x }$. Approximate how many years it takes for the number of hamburgers served to reach 77 million. Round to the nearest year.
A) $6 \mathrm { yr }$
B) $3 \mathrm { yr }$
C) $5 \mathrm { yr }$
D) $4 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the number of years it takes for the number of hamburgers served to reach 77 million, we set the function equal to 77 and solve for $x$:$$77 = 37.8e^{0.18x}$$Dividing both sides by 37.8 gives:$$2.037 = e^{0.18x}$$Taking the natural logarithm of both sides gives:$$\ln(2.037) = 0.18x$$Solving for $x$ gives:$$x = \frac{\ln(2.037)}{0.18} \approx 4$$Therefore, it takes approximately 4 years for the number of hamburgers served to reach 77 million.

Write the Word or Phrase That Best Completes Each Statement f(x)=37.8e0.18xf ( x ) = 37.8 e ^ { 0.18 x }f(x)=37.8e0.18x

Write the Word or Phrase That Best Completes Each Statement $f ( x ) = 37.8 e ^ { 0.18 x }$