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 $k$, substitute $x = 4.5$ (since $x$ is in hundreds of dollars and \$450 is spent) and $S = 2500$ into the equation $S = 20(1 - e^{kx})$. This gives $2500 = 20(1 - e^{4.5k})$. Solving for $k$ yields $k \approx -0.183$. To estimate sales for \$650 spent on advertising, substitute $x = 6.5$ and the value of $k$ into the original equation, which results in approximately 3508 units sold.

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

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