Question

The total amount spent by somite f(x)=−4.973x²+7123x+96.27

Answer 1

The total amount spent, represented by the function
`\( f(x) = -4.973x^2 + 7123x + 96.27 \)`, is given by the integral of the function over a specified range. The definite integral from
`\( x = a \) to \( x = b \)`provides the total expenditure in that range.

Step-by-step explanation:

To find the total amount spent, we need to calculate the definite integral of the given function
`\( f(x) = -4.973x^2 + 7123x + 96.27 \)` over a specific range. The definite integral represents the signed area under the curve between the given limits, in this case, from
`\( x = a \) to \( x = b \). Mathematically, it is denoted as \( \int_(a)^(b) f(x) \,dx \).`

In the provided function, the term
`\( -4.973x^2 \)`represents a downward-opening parabola, while the terms
`\( 7123x \) and \( 96.27 \)`contribute to the overall shape of the curve. The integral of this function over the specified range yields the net accumulation of spending.

To obtain the final result, numerical methods or calculus techniques, such as the fundamental theorem of calculus, can be employed to evaluate the definite integral. The outcome will be a precise numerical value that represents the total amount spent within the given range according to the function
`\( f(x) \)`.