The function f left parenthesis x right parenthesis equals 0.4 x squared minus 36 x plus 900 models the number of accidents, f(x), per 50 million miles driven as a function of a driver's age, x, in years, where x includes drivers from ages 18 through 72, inclusive. The graph of f is shown. Use the graph to identify two different ages for which drivers have the same number of accidents. Use the equation for f to find the number of accidents for drivers at each of these ages. . . . Question content area top right Part 1 0 100 0 1000 Age of Driver Number of Accidents f left parenthesis x right parenthesis equals 0.4 x squared minus 36 x plus 900 18 45 72
A coordinate system has a horizontal x-axis labeled 'Age of Driver' from 0 to 100 with vertical lines at 0, 16, 45 and 74 and a vertical y-axis labeled 'Number of Accidents' from 0 to 1000. A U-shaped curve that opens upward passes through the points (18, 382), (45, 90), and (72, 382). The curve is labeled f left parenthesis x right parenthesis equals 0.4 x squared minus 36 x plus 900. The curve is dashed from x = 0 to x = 18 and from x = 72 to 100. The curve is solid between x = 18 and x = 72. All coordinates are approximate. Question content area bottom Part 1 Identify two different ages for which drivers have the same number of accidents. Choose the correct answer below. A.x equals 45 comma x equals 72 x equals 45 comma x equals 72 B.x equals 18 comma x equals 72 x equals 18 comma x equals 72 C.x equals 18 comma x equals 0 x equals 18 comma x equals 0 D.x equals 18 comma x equals 45 x equals 18 comma x equals 45 Part 2 Find the number of accidents for drivers at each of these ages. enter your response here (Round to the nearest whole number as needed.) Choose the correct answer below.Find the number of accidents for drivers at each of these ages.(Round to the nearest whole number as needed.)
To solve the problem, we first need to identify the two different ages for which drivers have the same number of accidents based on the graph of the function ( f(x) = 0.4x^2 - 36x + 900 ).
From the description of the graph, it appears that the function has the same value (number of accidents) at two different ages: ( x = 18 ) and ( x = 72 ). Therefore, the correct answer for Part 1 is:
B. ( x = 18, x = 72 )
Next, we need to find the number of accidents for drivers at these ages using the function ( f(x) ).
Calculate ( f(18) ): [ f(18) = 0.4(18^2) - 36(18) + 900 ] [ = 0.4(324) - 648 + 900 ] [ = 129.6 - 648 + 900 ] [ = 129.6 + 252 ] [ = 381.6 ]
Rounding to the nearest whole number, ( f(18) \approx 382 ).
Calculate ( f(72) ): [ f(72) = 0.4(72^2) - 36(72) + 900 ] [ = 0.4(5184) - 2592 + 900 ] [ = 2073.6 - 2592 + 900 ] [ = 2073.6 - 1692 ] [ = 381.6 ]
Rounding to the nearest whole number, ( f(72) \approx 382 ).
Thus, the number of accidents for drivers at both ages ( 18 ) and ( 72 ) is approximately 382.