Suppose the number of Quickie hamburgers (in millions) served yearly can be modeled by $f ( x ) = 35.8 e ^ { 0.17 x }$ Approximate how many years it takes for the number of hamburgers served to reach 54 million. Round to the nearest year.
A) 2 yr
B) 3 yr
C) 1 yr
D) 4 yr

Question

Quizplus · Accepted Answer

To find the number of years it takes for the hamburgers served to reach 54 million, set $f(x) = 54$ and solve for $x$:  $54 = 35.8 e^{0.17x}$  Divide both sides by 35.8:  $1.5084 \approx e^{0.17x}$  Take the natural logarithm of both sides:  $\ln(1.5084) \approx 0.17x$  Solve for $x$:  $x \approx \frac{\ln(1.5084)}{0.17} \approx 2$  So, it takes approximately 2 years.

Suppose the Number of Quickie Hamburgers (In Millions) Served Yearly f(x)=35.8e0.17xf ( x ) = 35.8 e ^ { 0.17 x }f(x)=35.8e0.17x

Suppose the Number of Quickie Hamburgers (In Millions) Served Yearly $f ( x ) = 35.8 e ^ { 0.17 x }$