A garden with area of 5000 sq. feet requires 50 cubic yards of dirt. Express this information in terms of the function g

To express the given information in terms of the function \( g \), let's define \( g(A) \) as the function that calculates the number of cubic yards of dirt needed based on the area \( A \) of the garden in square feet. ### Given: - **Area of the garden (\( A \))**: 5000 square feet - **Volume of dirt required (\( D \))**: 50 cubic yards ### Relationship: We can establish a linear relationship between the area and the volume of dirt required. Since 5000 square feet requires 50 cubic yards of dirt, the function \( g(A) \) can be defined as: \[ g(A) = \frac{A}{100} \] ### Explanation: - **Calculation**: \[ g(5000) = \frac{5000}{100} = 50 \text{ cubic yards} \] This matches the given data. - **Interpretation**: For every 100 square feet of garden area, 1 cubic yard of dirt is needed. Therefore, the function \( g(A) \) calculates the required cubic yards of dirt by dividing the garden area by 100. ### Final Function: \[ g(A) = \frac{A}{100} \] **Where:** - \( A \) is the area of the garden in square feet. - \( g(A) \) gives the required volume of dirt in cubic yards. ### Example Usage: If you have a garden area of 2500 square feet, the required dirt would be: \[ g(2500) = \frac{2500}{100} = 25 \text{ cubic yards} \]