The sales $S$ (in thousands of units) of a cleaning solution after $x$ hundred dollars is spent on advertising are given by $S = 20 \left( 1 - e ^ { k x } \right)$. When $\$ 450$ is spent on advertising, 2500 units are sold. Complete the model by solving for $k$ and use the model to estimate the number of units that will be sold if advertising expenditures are raised to $\$ 650$. Round your answer to the nearest unit.
A) 3508 units
B) 6401 units
C) 5508 units
D) 2483 units
E) 8787 units

Question

Quizplus · Accepted Answer

To find $k$, use the given data: $S = 2500$ when $x = 4.5$ (since $x$ is in hundreds of dollars and $450$ dollars is spent). Substituting these values into the equation gives $2500 = 20(1 - e^{4.5k})$. Solving for $k$ yields $k \approx -0.183$. To estimate sales for $x = 6.5$ (\$650), substitute $x = 6.5$ and $k = -0.183$ into the original equation, resulting in approximately $3508$ units.

The Sales SSS (In Thousands of Units) of a Cleaning Solution After

The Sales $S$ (In Thousands of Units) of a Cleaning Solution After