The daily demand for ice cream cones at a price of $1.20 per cone is 50 cones. At a price of $2.20 per cone, the demand is 30 cones. Use linear interpolation to estimate the demand at a price of $1.50 per cone.

The estimated demand for ice cream cones at a price of $1.50 per cone is 44 cones using linear interpolation.

Linear interpolation can be used to estimate the demand at a price of $1.50 per cone based on the given data points.

Let, the price as "P" (in dollars) and the demand as "D" (in cones).

Given data points:

Price = $1.20, Demand = 50 cones

Price = $2.20, Demand = 30 cones

We want to estimate the demand at Price = $1.50.

First, calculate the demand change between the two price points:

Demand change = Demand at $2.20 - Demand at $1.20

Demand change = 30 - 50 = -20 cones

Now, calculate the price difference between the target price ($1.50) and the lower price ($1.20):

Price difference = Target Price - Lower Price

Price difference = 1.50 - 1.20 = 0.30

Next, calculate the proportional change in demand due to the price difference:

Proportional change = (Price difference / Price change) * Demand change

Proportional change = (0.30 / 1.00) * (-20) = -6 cones

Finally, estimate the demand at the target price:

Demand at target price = Demand at lower price + Proportional change

Demand at target price = 50 - 6 = 44 cones

Therefore, the estimated demand for ice cream cones at a price of $1.50 per cone is 44 cones using linear interpolation.

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Final answer:

Using linear interpolation, the estimated demand for ice cream cones at a price of $1.50 per cone is 44 cones.

Explanation:

To estimate the demand at a price of $1.50 per cone using linear interpolation:

1. Calculate the slope or rate of change of the demand by using the formula: slope = (change in demand) / (change in price).
2. Using the given data, calculate the slope as (30-50) / ($2.20-$1.20) = -20 / $1.00 = -20.
3. Then, use the slope and one of the given points to find the equation of the linear demand function. Let's use the point (50, $1.20).
4. The linear demand function is given by: demand = slope * (price - given price) + given demand.
5. Substituting the values, we have demand = -20 * (price - $1.20) + 50.
6. Finally, substitute the given price of $1.50 into the demand function: demand = -20 * ($1.50 - $1.20) + 50 = -20 * $0.30 + 50 = 44 cones.

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