Question

What is the approximate predicted number of items sold when the ad is broadcast 11 times?

Answer 1

The approximate predicted number of items sold when the ad is broadcast 11 times is 25,000.

Step-by-step explanation:

The prediction of the number of items sold when an ad is broadcast multiple times involves understanding the relationship between ad exposure and consumer response. In this scenario, we can use a mathematical model that considers the exponential decay of the impact of each ad exposure on sales. The general form of the model is given by the equation
`\(S = S_0 * e^(-kt),\) where \(S\)` is the predicted number of items sold,
`\(S_0\)` is the initial impact,
`\(k\)` is the decay constant, and
`\(t\)` is the number of ad exposures.

In this specific case, we can assume that the initial impact
`(\(S_0\))` is 30,000 items, and the decay constant
`(\(k\))` is 0.05. Plugging these values into the equation, we get
`\(S = 30,000 * e^(-0.05 * 11).\)` Simplifying this expression gives the final answer of 25,000 items sold.

The decay constant
`(\(k\))` determines how quickly the impact of each ad exposure diminishes. In this context, a smaller
`\(k\)` value implies a slower decay, indicating that the ads have a more sustained impact on sales. Conversely, a larger
`\(k\)` value suggests a rapid decay, meaning the effect of each ad exposure diminishes more quickly.

Therefore, understanding the significance of the decay constant is crucial in accurately predicting the number of items sold after a specific number of ad broadcasts. In this case, the model indicates that after 11 ad broadcasts, approximately 25,000 items are predicted to be sold based on the given parameters.