Question

You are running a food stand for a carnival. On the first night you expect to bring in $2000. Each night after the first, revenue will be about 70% of the previous night's revenue. To the nearest dollar, about how much revenue can the carnival anticipate on its 5th night in town? On the 5th night, the carnival can expect $______in revenue .

Answer 1

Using the exponential decay formula, the expected revenue on the fifth night of the carnival is calculated to be $480.20, which rounds to $480.

Step-by-step explanation:

To calculate the expected revenue on the fifth night, we need to apply the principle of exponential decay, as the revenue is decreasing by a constant percentage each night. The formula to use is revenue = initial revenue * (rate of decay)^number of periods.

In this case, the initial revenue is $2000, the rate of decay is 70% (or 0.7 when expressed as a decimal), and the number of periods is 4 nights after the first night.

The calculation for the fifth night's revenue is: $2000 * (0.7)^4 = $480.20. Rounded to the nearest dollar, the revenue on the fifth night is expected to be $480.