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) 2160 units
D) 5663 units
E) 8787 units

Question

Quizplus · Accepted Answer

To solve for $k$, we use the given data: when $x = 4.5$ (since $x$ is in hundreds of dollars), $S = 2500$. Substituting these values into the equation gives $2500 = 20(1 - e^{4.5k})$. Solving for $k$ yields $k \approx -0.183$. Using this value of $k$ and $x = 6.5$ (for $650), the model estimates $S \approx 3508$ units.

The Sales S (In Thousands of Units) of a Cleaning S=20(1−ekx)S = 20 \left( 1 - e ^ { k x } \right)S=20(1−ekx)

The Sales S (In Thousands of Units) of a Cleaning $S = 20 \left( 1 - e ^ { k x } \right)$