Chapter 4.3, Problem 55PS

Solution

To determine: The number of object C that were shipped in the year 2002.

  $895.03$ millions

Given information:

The number of object C’s that was shipped since 1997 can be estimated by the model given below:

  $y=1.28e^{1.31x}$

Here, $y$ is in millions and $x$ represents the number of year since 1997.

Concept used:

If $y$ is the function of $x$ , then to find the value of $y\left(x\right)$ at $x=x_0$ , substitute $x=x_0$ in the given function.

Calculation:

Observe that 2002 comes 5 years after 1997; therefore, the value of $x$ is 5 years. To find the number of object C that were shipped in the year 2002, substitute $t=5$ in the equation $y=1.28e^{1.31x}$ :

  $\begin{array}{c}y=1.28e^{1.31\left(5\right)}\\ =1.28e^{6.55}\\ =1.28\left(699.24\right)\\ =895.03\end{array}$

Conclusion:

Hence, in the year 2002, approximately $895.03$ millions of object C are shipped.