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 + 950 ).
From the description of the graph, we see that the function has the same value at two different ages: ( x = 26 ) and ( x = 64 ). Therefore, the correct answer for Part 1 is:
A. ( x = 26, x = 64 )
Next, we need to find the number of accidents for drivers at each of these ages using the function ( f(x) ).
-
Calculate ( f(26) ):
[
f(26) = 0.4(26^2) - 36(26) + 950
]
[
= 0.4(676) - 936 + 950
]
[
= 270.4 - 936 + 950
]
[
= 270.4 + 14
]
[
= 284.4
]
-
Calculate ( f(64) ):
[
f(64) = 0.4(64^2) - 36(64) + 950
]
[
= 0.4(4096) - 2304 + 950
]
[
= 1638.4 - 2304 + 950
]
[
= 1638.4 - 1354
]
[
= 284.4
]
Both calculations yield approximately ( 284.4 ). Rounding to the nearest whole number gives us:
284 accidents for both ages ( x = 26 ) and ( x = 64 ).
Thus, the answer for Part 2 is:
284 (rounded to the nearest whole number as needed).