Choose the one alternative that best completes the statement or answers the question.
-Suppose the number of Quickie hamburgers (in millions) served yearly can be modeled by $f ( x ) = 39.6 e ^ { 0.14 x }$. Approximate how many years it takes for the number of hamburgers served to reach 152 million. Round to the nearest year.
A) $9 \mathrm { yr }$
B) $11 \mathrm { yr }$
C) $10 \mathrm { yr }$
D) $12 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the number of years it takes for the number of hamburgers served to reach 152 million, we set the function equal to 152 and solve for $x$:$$152 = 39.6e^{0.14x}$$Dividing both sides by 39.6 gives:$$3.84 = e^{0.14x}$$Taking the natural logarithm of both sides to solve for $x$:$$\ln(3.84) = 0.14x$$$$x = \frac{\ln(3.84)}{0.14} \approx 10$$Therefore, it takes approximately 10 years for the number of hamburgers served to reach 152 million.

Choose the One Alternative That Best Completes the Statement or Answers